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Jet Speed Measurement by Correlation of Optical Signals
©
Co p\"l'ig hl IF .\ C 1ll 'l lflllll t' nl ati o ll a nd .\lII o lll ati o ll in the Pa per. R ubbt' l . PL.I'Iti(, dnd Po" I1 H.'1 i',lIio l1 Indu 'i tri e'l .. \nt ht' l p. B t' I ~illlll I ~ I X :\
JET SPEED MEASUREMENT BY CORRELATION OF OPTICAL SIGNALS Ph . Bolon*, E. Moisan* and ':":' / I/ I !I!II!
J.
Sabater**
" C'.\R.S. SOIll ! -.\/ lIr! l l/ -d "i / h"'.I. F ra l/i/' I'! A/J/JlilJlI il'. O nll.". Fml/l l'
d D /Hlqll/, TMoriqll/'
Abstract. Methods for determining jet- flow velocity directly and on-line are few in number. All those involving the introduction of a sensor in the flow have to be avoided because they generate disturbances in the fluid stream. The method presented in the paper is based on the cross-correlation of optical signals. It allows a contact less measurement . Principles of the optical device and of the correlation method are briefly described . Then we present experimental results obtained on laboratory apparatus and on industrial papermachines. The optical sensor can easily be installed on an industrial machine for determinin g the cross-motion velocity profile for instance. Keywords . Correlation methods, headbox, jets, optics, pulp industry, sensors, signal processing, stochastic processes, time delay estimation, velocity control. INTRODUCTION
than transmitted light, so only one side of the surface of the jet has to be accessible. Therefore the apparatus can easily be installed on an industrial machine without distur bing the production . The device described below allows the jet speed to be measured without any contact. In association with simple signal processing techniques (spectral analysis, coherence ... ) it can a lso provide information about some physical c h aract e ristics of the jet, such as f locculation [5].
One of the parameters which papermakers have to solve is the regulation of the basis weight in the cross-machine direction . As a matter of fact, it depends on the homo g eneity of the velocity profile of the pulp jet in that direction. On the other hand, some recent paper machine automation techniques include jet speed as a parameter [1], [2] . Therefore, it becomes interesting to develop a precise method which yields the speed of the stockjet at the outlet of the headbox, on line and without disturbin g the industrial process.
In this paper, we succinctl y de scribe the measurement apparatus ( o ptica l sens o r and electronic correlator). Th en, we present experimental results obt ain e d a t t he Cen tr e Technique du Papier ( Gren o ble, F r an ce ) a nd on industrial papermachines.
Among the available techniques, we can use ultrasounds [3], or fluctuations of electrical resistivity [4]. For re a sons of transducer efficiency, these methods ha ve to be used with pipe flows or insi de th e headb o x. But it is well known that the c h ar a ct e ristics of the jet are modified between th e slices and the wire (contraction, re f l o ccula ti o n [ 5]) . Th e refore, the measurement sh o ul d be c a rried out at a position clo se t o t h e i mpa ct o f the j et onto the wire.
PRI NCIPLE OF JET SPEED 11EASUREHENT BY CROS S CORRELAT I O~ Let V be the vel o cit y of th e j et which we suppose moving in it s p l a ne wi t hou t defo r ma t ion . We illuminat e two po int s A a nd B of its su rface, with AB parall e l t o V . Two iden t ical optical devices collect th e li gh t backsca tt e r ec at A and B on two li g ht detector s (fig . l) .
Optical techniques sat isfy t he c o ndition of non contact. La ser Dopp l e r Velocimetr y methods (LDV) [6] c a nno t be e a s ily use d in an indus trial environment . Th e y nee d a rat h er complex and expens i ve e q ui pme n t . Noreover, these method s are no t fitt e d with t h e particle concentrations commo nl y u se d in the pulp jets .
X(t)
Y (t)
I
o
The method pr op ose d in t h e pape r is based on the cross correl a tion of op tic a l si g nals. Th is techni qu e ne eds on l y simp l e d evic e s. iH th a pul p j e t, the p r ob l em i s more complex than in the case of pa pe r s h e e t [ 7] o r railwa y [8] o r c o l d -r olled s t eel [9] , be ca use of t h e tu r bu le nce of t he flow . The op t i c a l sensor n re se nte d he r e uses backsca tt e r ed l ight r a t h er
A
B
Fi g . 1. Pri n ci p le of me asu r emen t
43
44
Ph. Bo l on, E . Mo is an a nd J . Sa ba t er
Let x(t) and y(t) by the a.c. components of the detector signals and ryx(~) an estimation of their cross-correlation function given by : ryx(t.) =
4-
LT
y(t)
x(t-~
dt
Eq.1
T is the integration time (measurement time) Let D be the value of the distance AB. The transit time between A and B is = so y(t) is nearly identical with x(t) with a delaye. Hence r:!x( to) presents a maximum at the time lag t: = tI. After computation of ryx(~)' the peak abscissa is an estimate of the transit time from which we obtain an estimation of the jet speed.
e- %'
THE OPTICAL DEVICE The light source used in the sensor is a low power He Ne Laser whose beam is split in two parallel beams by a prism assembly P (fig.3). An astigmatic optical system S gives on the jet surface two ellipsoidal spots of dimensions 0.1 x 5 mm. The advantage of the laser source is its great spatial coherence giving the possibility to obtain small highly luminous spots with a great depth of field without requiring complex devices. A part of the backscattered light of the two spots is focused on two different silicon cells by an aspheric lens L.
Because of the randomness of the signals, the cross-correlation function cannot be perfectly known. The true function is blurred by the estimation noise, so an error on the position of the maximum may occur (fig. 2).
The apparatus is set so that the incident beams are orthogonal to the jet surface. The influence of surface phenomena (ripples, droplets ••• ) can be ruled out by separating the emission and reception direction. Here, the angle between these direction is 25°.
~.
Distance D is adjustable from the outside of the device with a micrometric screw. The width of the spots in the speed direction is 0.1 mm. This allows the knowledge of the D value with a relative precision more accurate than 1 %. In the cross-machine direction, the length of the spots is about 5 mm long. The distance between the sensor and the jet surface is about 60 mm, with a depth of field ± 10 mm. The parallelism of the AB axis and the speed vector has to be set so that the relative error on the distance is less than 1 %. With an angular misalignment m, the relative error is e = 1 - cos m , so that the required condition is satisfied with m(7°.
Estimation of the cross-correlation function.
The precision of the speed measurement depends w on the relative sharpness of the peak "&' and on the degree of similarity of x and y (i.e. their correlation coefficient) and on the precision of the estimation of the correlation function. Let a be the average size of the flocs in the w a jet. Then the sharpness is 9= D where D is the distance between the laser spots. Therefore, the precision tends to increase with D. However, because of the turbulence of the flow, the correlation between x and y decreases when D is too large, and then the peak vanishes in the estimation noise. The choice of a distance D results from a compromise between these two effects. With the velocities and fiber consistencies commonly used in paper machines, the optimal distance ranges from 10 to 20 mm. The quality of the estimation of the correlation function increases with the integration time T. However, T should be small enough so that the speed fluctuations could be tracked. A precision of 1 % with 5 measurements per second seems to be an interesting objective.
All these arguments show that the positioning of the sensor is not critical.
As tiqmat ic Prism syslem assemtiy
! ~.
Pulp jet
\-
The optical device
Jet Speed Measurement THE ELECTRONIC CIRCUIT The electronic circuit has to compute the estimation of the correlation function and to determine the position of its maximum. The computation of the speed can be performed either analogically or digitally (with an arithmetic co-processor for instance). If we are interested only in the fluctuations of the velocity around a mean value, a digitalto-analog conversion of the address of the maximum is a sufficient indication.
45
Let V0 be the vfjloci ty at the center flow and eo = In the frequency transformation F 0 is characterized complex gain g( f) which can be put form : -i2n f6 0 g(f) = G(f) e _-:-_ _ _ _ _ ------A---deformation and speed transport at dipersion of structures velocity Vo
v .
~"'---
of the domain, by its in the Eq.3
In these conditions the statistical characteristics of the estimation are given by Eq.4 and Eq.5.
We know [10] that the computation of the correlation function does not require high accuracy, provided that the correlation between signals X and Y is good. We use an actual correlator rather than a delay-locked loop because of the sensitivity of the latter method to mechanical vibrations of the sensor. A correlator is slower but more robust, even if it does not operate in real time, as far as the signal bandwidth is concerned. It is then possible to use only the sign of the signals. This drastically simplifies the quantization and multiplication operations without increasing the estimation errors too much [7].
bias :
The results which are presented below were obtained either with a correlator using 4-bit quantization or with a correlator using 1-bit quantization.
Note that the integral at the denominator is proportional to the second derivative, with respect to r, of the cross-correlation function. Hence, it is representative of the "sharpness" of the peak. On the other hand, we remark that the variance is inversely proportional to the integration time T. The variance decreases when the coherence function increases. As a matter of fact, parameters GR,GI,C, depend on the distance D. Eq.4 and 5 are a mathematical formulation of the previous remarks (see section "Principle of Measurement").
RESULTS Theoretical results. Let X(t) and Y(t) be the random signals delivered by the optical sensor The statistical dependance between X and Y can be modelled as in Eq.2 : Y(t)
=F
[X(t)] + N(t)
Eq. 2
X and N are two zero-mean stochastic processes jointly gaussian stationnary and ergodic in the wide sense. F is a linear transformation representing transport and deformation of structures within the jet. N is an additive independant noise, representing coming out or vanishing structures.
PRESSURE SENSOR
Eq.4
b
Eq.5
f denotes the frequency. ~ and GI are real and imaginary part of G(f) respectively. T is the integration time, Sxx( f) the power spect rum of X, C( f)\ the modulus of the coherence function of X and Y.
I
EXPERIMENTAL RESULTS Experiments were conducted with following conditions : - speed : 2 m/s to 8 m/s - fiber consistency : 1 g/l to 15 g/l - thickness of the jet : 10 mm to 20 mm
OPTICAL SENSOR + CORRELATOR / y / X
H
L=1m
VALVE
~.
FLOWMETER
Diagram of the experimental device
Ph. Bolon, E. Moisan and J. Sa ba ter
46
In order to compare the correla tion method with other conven tional instrum ents (electr omagnet ic flowme ter, impact pressu re sensor .•• ) we used an experim ental device built up at the Centre Techniq ue du Papier (Greno ble). The appara tus compri ses a vat having constan t level, an electro magne tic flowme ter, a flow regula ting valve, a pipe of square section . The outlet is compose d of a taper whose geometry can be varied (fig.4) . Apart from its width, the jet is identic al with those obtaine d on indust rial paperm achines, as far as speed, thickn ess, fiber consistenc y are concern ed. In order to rule out the effects of finite width, all measure ments were perform ed in the middle of the jet (in the cross-m otion directi on).
We have, in fig. 5
AQ
Qo
=
6.95 % and
Av Vo
7.05 %
Since it is diffi c ult to obtain a perfec tly steady flow rate, we may say that there is a good agreem ent between the two determ ination s. If we examine the fluctua tions of the measured veloci ty, we remark that the estima tion errors are compri sed within the limits ± 1.1 % Fig. 6 presen ts a simila r experim ent conduc ted in other condit ions. L
VELOCITY
Compar ison with an electro magne tic flowme ter. By varying the positio n of the flow regula ting valve, we genera te fluctua tions in the flowrate which are measure d by an electro magne tic flowme ter. These variati ons are compare d with those measure d by means of the optica l sensor . Fig. 5 shows the evoluti on of the flowra te and of the measure d veloci ty as a functio n of the time. Let 4Q and 4v be the variati ons of the flowrat e and of the veloci ty respec tively. Since the perpen dicular section in the flowmeter and in the pulp jet are di fferea t, we will examine the relativ e variati ons ~ and
I~
R
FLOWRATE
Qo
AV
-"
Vo 1 I
t ··
I I ·I
I·T T
1---+'-.,,- -
.. •
.• .
~~
.- ~ ~
. :T
F1g. 6. Compar 1son flowrat e - veloci ty Experim ental conditi ons : 5 .7 m/ s - jet spe ed - pulp comp osition : 70 % softwoo d, 30 % hardwo od - consist ency : 1 g/ l distanc e D : 6 mm - Correla tor using 4-bit quanti zation Averag ing time 64 ms The relativ e variat i ons are : .
,~
,
1----·-· -,-- . ---'---:---:----
AQ Qo
=
7.3 %
and
AV=7 . 2% Vo
,
Fig . 5 . Compar is on flowra te - veloci ty Experim ental conditi ons : 4.9 m/ s - jet speed - pulp compos ition : 60 % softwoo d, 40 %hardwoo d - consist ency : 10 g/ l - distanc e D : 5 mm - Correl ator uSing I-bit quanti zation Averag ing time 100 ms
The estima tions errors are larger (± 2.4 %) than in the previ ous case. This is caused by the short integra tion time (64 ms instead of 100 ms) and by the low consist ency. As a matter of fact, the state of floccu lation is a functio n of the fiber concen tration and a low floccu lation rate induces a poor correla tion between backsc attered signals X and Y. However, we should notice that this consist enc y is unusua l on paperm achines .
Jet Speed Measurement Influence of the distance between laser spots We know [11] that, because of shear stresses, large floes tend to be present at the center of the flow, where velocity gradient and turbulence intensity are minimum, whereas smaller ones are near the edges. Because of the mean velocity profile (in the z-direction), small floes move more slowly thna larger ones. For reasons of penetration of the laser beam, the measured velocity is less than the speed at the center of the jet. However, this drawback disappears if we increase the distance between laser spots D. As a mat ter of fact, the mechanical resistance of small floes is less than the one of large floes. Therefore, for large distances D, only large floes give a contribution to the correlation peak. Then, the velocity at the center of the flow can be measured by this method, with a sufficient precision. Fig. 7 shows the measured velocity vs distance D. The experimental conditions were : - jet speed - consistency - thickness of the jet
47 U(t)
Let :
=
Uo + u
Eq.7
where Uo is the mean velocity and u the turbulence term. We have P(t)
1" '2 \ (U o2 + 2uU o + u 2 )
Hence the mean pressure is :
oi
where is the variance of u and I the turbulence intensity. Because of the fibers, the turbulence intensity is low [5]. Then the corrective term can be neglected and the mean pressure yields a direct measurement of the jet veloci ty. Fig. 8 shows a comparison between results obtained with the optical sensor and wi th the pressure sensor.
8 m/s 8.8 g/l 13 mm
VELOCI TT
SO
VELOC ITY : M/S
7.5
PRESSURE SENSOf ""-{ -V::--; -=-_ ,J ( MI5)
J1J--(r :P;;"~~ENSO~ 1
.40
DI STANCE
1'. 10
7.0
~.
T.
DISTANCE D:MM I
5 ~.
10
•
.
(MM)
20
Comparison optical sensor - pressure sensor
Experimental conditions
I
15
20
Influence of the distance D
The shape of this curve is fairly typical. The importance of the transient zone (small distances) depends on the "roundness" of the mean velocity profile in the z-direction. Comparison with a pressure sensor. A pressure sensor is placed in the circuit as indicated in Fig. 4. It provides an electrical signal proportional to the total impact pressure. In a zone where static pressure is identical with atmospheric pressure, the instantaneous impact pressure is : Eq.6 where
Eq.8
U(t) is the instantaneous velocity ~ is the mass per unit volume of the fluid.
- jet speed : 5.5 m/s - thickness of the jet : 20 mm - pulp composition : 60 % softwood, 40 % hardwood - consistency : 10 g/l The correlation functions were computed over a large integration time (T = 15 s), so that the estimation error on the transit time can be reduced to 1 sampling period. In those conditions, the precision of the velocity estimation was ~.
.. DO
The velocity measured by means of the pressure sensor is Vp = 5.494 m/so If we examine Fig. 8, we remark the typical shape of the curve velocity vs distance D. But if we consider the results obtained with distances larger than or equal to 10 mm, we notice that the agreement between the two determinations is better than .5 % ! If we compute the mean value of the results obtained with the five largest distances, we obtain Vm = 5.484 m/so The agreement is better than .2 %.
48
Ph. Bolon, E. Moisan and J. Sabater
Discussion. The quality of the paper sheet depends on the flocculation, and especially on large flocs. This is one of the reasons why it is interesting to measure the- speed of these structures. Since the optical sensor uses backscattered light rather than transmitted light, it is sensitive to external phenomena. However, we saw that it was possible to access to the speed of the internal phenomena by increasing the distance between the laser spots. The reason why this speed measurement method works is that the velocity profile is rather flat in the z-direction. Even if the penetration of the laser beam is low, structures moving at maximum velocity are illuminated. Fig. 9 shows such a velocity profile, obtained bv means of a Pitot tube. VE!..OC I TY (M IS)
8,5
,"/--
•
8, 0
'-'-1' -'-.-.'-.. t I
Therefore, speed and ditions of cision of second.
is becomes possible to measure jet velocity fluctuations in the conan industrial machine with a pre1 % and with 10 measurements per
APPL I CATI ONS •
The speed measurement mehtod presented here was tested on different industrial papermachines. Fig. 10 shows a cross-correlation function obtained with the optical sensor on an industrial pul ~ jet.
31
u. ,
~I u. ,
1,5
Results presented in Fig. 5 and Fig. 6 seem to prove that a precision of 1 % can be approached with an integration time T = 100 ms. However, results are better than they seem to be, because the true velocity is itself slightly unstable. This unstability was pointed out by studying the instantaneous impact pressure. By filtering the pressure signal in the frequency band 0-5 Hz, we rule out the most part of fluctuations caused by the turbulence. In those conditions, signal fluctuat ions are of the order of 2.4 %. Since the precision of the sensor is 0.5 %, the velocity unstability is estimated to be about 1 %. This unstability is probably due to the design of the hydraulic circuit.
~I
e-'
~ I,
-(
,
'
J
-5
~.
,
I
z- 0 iRECTlOIIJ -
o
.5
J
,
'
,
,
J
POSITION (MM) Velocity profile in z-direction
Experimental conditions : - jet speed : 8 m/s - thickness of the jet : 13 mm - pulp : Bleached Kraft - consistency: 0.15 g/l
.. Fig. 10. Example of cross-correlation function
Similar curves were obtained in different conditions of speed and thickness. We notice in Fig. 9 that in a zone covering 8 cm in zdirection, speed variations are less than 1 %. With usual consistencies, fibers and flocs tend to be opposed to the velocity gradient [11), and then they increase the flatness of the velocity profile. These arguments show that the optical sensor can be used for measuring the absolute value of the jet speed in industrial conditions. If we are interested in tracking velocity fluctuations (for production optimization for instance), we need a given relative precision, say 1 %, with an integration time as short as possible. In these conditions, good results are obtained with large signal bandwidths and high correlation coefficients. As a matter of fact, if the consistency increases, flocs become largecand more resistant. Therefore, the signal bandwidth decreases and the correlation coefficient increases. It seems that the latter effect get the better of the other.
The correlation function is computed in the range 256 512 At, where 4t is the sampling period. The distance between laser spots is 19 mm and the jet speed is 640 m/min. We notice that the correlation peak is rather blunt, compared wi th sharpness of peaks obtained on papersheets [7).
4t -
Wi th this optical sensor, it is easy to determine the cross-motion velocity profile of the pulp jet. The support of the sensor is installed on a guiding rail (see Fig .12). It can be moved above the jet in both forward and cross-machine directions. There is no contact and the production is not disturbed. Fig. 11 shows a cross-motion velocity profile obtained in these conditions. The smooth curve (dotted line) is a parabolic regression. We notice that this machine presents a slightly asymetric profile. The fluctuations around the regression curve are caused either by the adjustment of the distance between the slices or by the hydraulic circuit up-stream of the slices.
Jet Speed Measurement
JET VELOCITr
CROSS-MOTION DIRECTION --
Fig. 11. Cross motion velocity profile on an industrial papermachine.
Fig. 12. Jet Speed Measurement on an Industrial Papermachine
49
Ph. Bolon, E. Moisan and J. Sabater
50
CONCLUSION Based on the cross-correlation of backscattered optical signals, the method proposed in the paper (correlation method) allows the jet speed to be measured without any contact. Experiments conducted at the Centre Technique du Paper and on papermachines show that, under the conditions of industrial production, speed measurement can be performed with a precision of the order of 1 %. The bandpass of such a velocimeter is large enough, so that it can be introduced in control systems driving the machine speed. The determination of the cross-motion velocity profile is obviously impossible by means of total head measurements in the box. Besides, impact pressure measurements cannot be carried out without disturbing the production. Then, the correlation method is an attractive solution to this problem, whose feasibility has been proven on different industrial papermachines.
[7] S. BAUDUIN, Ph. BOLON. A Paper Sheet Contactless Linear Speed Measurement. Proc. of 4th IFAC Conf. on Instrum. and Autom. in Paper, Rubber and Polymer Ind. (PRP4). Pergamon Press. Ghent. 3-5 June 1980. [8] G. SPIES, H. MEYR, J. BOHMANN. Real-Time Estimation of Moving Time Delay. Proc. of the IEEE Conf. ICASSP, Paris, 3-5 May 82. [9] 1. ANDERNO, A. SJOLUND. Laser Velocity Meter with Correlation Technique. Acta IMEKO, pp. 23-27, 1979. [10] Ph. BOLON, J .L. LACOUME. Speed Measurement by Cross-Correlation. Theoretical Aspects and Application in the Paper Industry. To be published in IEEE Trans. on Acoustics, Speech and Signal Proc., 1983. [11] G. DUFFY et al. making Fibers in BPBIF. Preprints Research Symp., Sept. 1977-.--
Hydrodynamics of PaperWater Suspension. Congo of the 6th Fundamental Oxford, Sess. 3, 18-23
- 0 -
ACKNOWLEDGEMENTS The authors wish to thank Messr Bauduin, Lafaverges and Palassof, of Centre Technique du Papier, for their active cooperation during this study.
REFERENCES [1] B. LEBEAU et al. Non Interacting Multivariable Papermachine Headbox Control Some Comparison with Classical Loops. Proc. of 4th IFAC Coni. on Instrum. and Autom. in Paper, Rubber and Polymer Ind. (PRP4). Pergamon Press. Ghent. 3-5 June 1980. [2] F.M. D'HULSTER et al. Application of Several Parameter - Adaptive Controllers to a Paper Machine Headbox. Proc. of 4th IFAC Conf. on Instrum. and Autom. in Paper, Rubber and Polymer Ind. (PRP4). Pergamon Press. Ghent. 3-5 June 1980. [3] L.C. LYNNWORTH. Clamp-on Ultrasonic Flowmeters ... Limations and Remedies. Instrumentation Technology, Sept. 75, pp. 37-44. [4] K.H. ONG, M.S. BECK. Slurry Flow Velocity Concentation and Particle Size Measurements using Flow Noise and Correlation Techniques. Measurements and Control. Vol. 8, Nov.1975. [5] Ph. BOLON, J. SABATER, S. BAUDUIN. A Contribution to the Study of the Stockjet as it leaves the Flowbox. To be published in Tappi Journal (1983). [6] T.S. DURRANI, C.A. GREATED. Laser Systems in Flow Measurement. Plenum Ed. 1979.
Co p\"l'ig hl IF .\ C 1ll 'l lflllll t' nl ati o ll a nd .\lII o lll ati o ll in the Pa per. R ubbt' l . PL.I'Iti(, dnd Po" I1 H.'1 i',lIio l1 Indu 'i tri e'l .. \nt ht' l p. B t' I ~illlll I ~ I X :\
JET SPEED MEASUREMENT BY CORRELATION OF OPTICAL SIGNALS Ph . Bolon*, E. Moisan* and ':":' / I/ I !I!II!
J.
Sabater**
" C'.\R.S. SOIll ! -.\/ lIr! l l/ -d "i / h"'.I. F ra l/i/' I'! A/J/JlilJlI il'. O nll.". Fml/l l'
d D /Hlqll/, TMoriqll/'
Abstract. Methods for determining jet- flow velocity directly and on-line are few in number. All those involving the introduction of a sensor in the flow have to be avoided because they generate disturbances in the fluid stream. The method presented in the paper is based on the cross-correlation of optical signals. It allows a contact less measurement . Principles of the optical device and of the correlation method are briefly described . Then we present experimental results obtained on laboratory apparatus and on industrial papermachines. The optical sensor can easily be installed on an industrial machine for determinin g the cross-motion velocity profile for instance. Keywords . Correlation methods, headbox, jets, optics, pulp industry, sensors, signal processing, stochastic processes, time delay estimation, velocity control. INTRODUCTION
than transmitted light, so only one side of the surface of the jet has to be accessible. Therefore the apparatus can easily be installed on an industrial machine without distur bing the production . The device described below allows the jet speed to be measured without any contact. In association with simple signal processing techniques (spectral analysis, coherence ... ) it can a lso provide information about some physical c h aract e ristics of the jet, such as f locculation [5].
One of the parameters which papermakers have to solve is the regulation of the basis weight in the cross-machine direction . As a matter of fact, it depends on the homo g eneity of the velocity profile of the pulp jet in that direction. On the other hand, some recent paper machine automation techniques include jet speed as a parameter [1], [2] . Therefore, it becomes interesting to develop a precise method which yields the speed of the stockjet at the outlet of the headbox, on line and without disturbin g the industrial process.
In this paper, we succinctl y de scribe the measurement apparatus ( o ptica l sens o r and electronic correlator). Th en, we present experimental results obt ain e d a t t he Cen tr e Technique du Papier ( Gren o ble, F r an ce ) a nd on industrial papermachines.
Among the available techniques, we can use ultrasounds [3], or fluctuations of electrical resistivity [4]. For re a sons of transducer efficiency, these methods ha ve to be used with pipe flows or insi de th e headb o x. But it is well known that the c h ar a ct e ristics of the jet are modified between th e slices and the wire (contraction, re f l o ccula ti o n [ 5]) . Th e refore, the measurement sh o ul d be c a rried out at a position clo se t o t h e i mpa ct o f the j et onto the wire.
PRI NCIPLE OF JET SPEED 11EASUREHENT BY CROS S CORRELAT I O~ Let V be the vel o cit y of th e j et which we suppose moving in it s p l a ne wi t hou t defo r ma t ion . We illuminat e two po int s A a nd B of its su rface, with AB parall e l t o V . Two iden t ical optical devices collect th e li gh t backsca tt e r ec at A and B on two li g ht detector s (fig . l) .
Optical techniques sat isfy t he c o ndition of non contact. La ser Dopp l e r Velocimetr y methods (LDV) [6] c a nno t be e a s ily use d in an indus trial environment . Th e y nee d a rat h er complex and expens i ve e q ui pme n t . Noreover, these method s are no t fitt e d with t h e particle concentrations commo nl y u se d in the pulp jets .
X(t)
Y (t)
I
o
The method pr op ose d in t h e pape r is based on the cross correl a tion of op tic a l si g nals. Th is techni qu e ne eds on l y simp l e d evic e s. iH th a pul p j e t, the p r ob l em i s more complex than in the case of pa pe r s h e e t [ 7] o r railwa y [8] o r c o l d -r olled s t eel [9] , be ca use of t h e tu r bu le nce of t he flow . The op t i c a l sensor n re se nte d he r e uses backsca tt e r ed l ight r a t h er
A
B
Fi g . 1. Pri n ci p le of me asu r emen t
43
44
Ph. Bo l on, E . Mo is an a nd J . Sa ba t er
Let x(t) and y(t) by the a.c. components of the detector signals and ryx(~) an estimation of their cross-correlation function given by : ryx(t.) =
4-
LT
y(t)
x(t-~
dt
Eq.1
T is the integration time (measurement time) Let D be the value of the distance AB. The transit time between A and B is = so y(t) is nearly identical with x(t) with a delaye. Hence r:!x( to) presents a maximum at the time lag t: = tI. After computation of ryx(~)' the peak abscissa is an estimate of the transit time from which we obtain an estimation of the jet speed.
e- %'
THE OPTICAL DEVICE The light source used in the sensor is a low power He Ne Laser whose beam is split in two parallel beams by a prism assembly P (fig.3). An astigmatic optical system S gives on the jet surface two ellipsoidal spots of dimensions 0.1 x 5 mm. The advantage of the laser source is its great spatial coherence giving the possibility to obtain small highly luminous spots with a great depth of field without requiring complex devices. A part of the backscattered light of the two spots is focused on two different silicon cells by an aspheric lens L.
Because of the randomness of the signals, the cross-correlation function cannot be perfectly known. The true function is blurred by the estimation noise, so an error on the position of the maximum may occur (fig. 2).
The apparatus is set so that the incident beams are orthogonal to the jet surface. The influence of surface phenomena (ripples, droplets ••• ) can be ruled out by separating the emission and reception direction. Here, the angle between these direction is 25°.
~.
Distance D is adjustable from the outside of the device with a micrometric screw. The width of the spots in the speed direction is 0.1 mm. This allows the knowledge of the D value with a relative precision more accurate than 1 %. In the cross-machine direction, the length of the spots is about 5 mm long. The distance between the sensor and the jet surface is about 60 mm, with a depth of field ± 10 mm. The parallelism of the AB axis and the speed vector has to be set so that the relative error on the distance is less than 1 %. With an angular misalignment m, the relative error is e = 1 - cos m , so that the required condition is satisfied with m(7°.
Estimation of the cross-correlation function.
The precision of the speed measurement depends w on the relative sharpness of the peak "&' and on the degree of similarity of x and y (i.e. their correlation coefficient) and on the precision of the estimation of the correlation function. Let a be the average size of the flocs in the w a jet. Then the sharpness is 9= D where D is the distance between the laser spots. Therefore, the precision tends to increase with D. However, because of the turbulence of the flow, the correlation between x and y decreases when D is too large, and then the peak vanishes in the estimation noise. The choice of a distance D results from a compromise between these two effects. With the velocities and fiber consistencies commonly used in paper machines, the optimal distance ranges from 10 to 20 mm. The quality of the estimation of the correlation function increases with the integration time T. However, T should be small enough so that the speed fluctuations could be tracked. A precision of 1 % with 5 measurements per second seems to be an interesting objective.
All these arguments show that the positioning of the sensor is not critical.
As tiqmat ic Prism syslem assemtiy
! ~.
Pulp jet
\-
The optical device
Jet Speed Measurement THE ELECTRONIC CIRCUIT The electronic circuit has to compute the estimation of the correlation function and to determine the position of its maximum. The computation of the speed can be performed either analogically or digitally (with an arithmetic co-processor for instance). If we are interested only in the fluctuations of the velocity around a mean value, a digitalto-analog conversion of the address of the maximum is a sufficient indication.
45
Let V0 be the vfjloci ty at the center flow and eo = In the frequency transformation F 0 is characterized complex gain g( f) which can be put form : -i2n f6 0 g(f) = G(f) e _-:-_ _ _ _ _ ------A---deformation and speed transport at dipersion of structures velocity Vo
v .
~"'---
of the domain, by its in the Eq.3
In these conditions the statistical characteristics of the estimation are given by Eq.4 and Eq.5.
We know [10] that the computation of the correlation function does not require high accuracy, provided that the correlation between signals X and Y is good. We use an actual correlator rather than a delay-locked loop because of the sensitivity of the latter method to mechanical vibrations of the sensor. A correlator is slower but more robust, even if it does not operate in real time, as far as the signal bandwidth is concerned. It is then possible to use only the sign of the signals. This drastically simplifies the quantization and multiplication operations without increasing the estimation errors too much [7].
bias :
The results which are presented below were obtained either with a correlator using 4-bit quantization or with a correlator using 1-bit quantization.
Note that the integral at the denominator is proportional to the second derivative, with respect to r, of the cross-correlation function. Hence, it is representative of the "sharpness" of the peak. On the other hand, we remark that the variance is inversely proportional to the integration time T. The variance decreases when the coherence function increases. As a matter of fact, parameters GR,GI,C, depend on the distance D. Eq.4 and 5 are a mathematical formulation of the previous remarks (see section "Principle of Measurement").
RESULTS Theoretical results. Let X(t) and Y(t) be the random signals delivered by the optical sensor The statistical dependance between X and Y can be modelled as in Eq.2 : Y(t)
=F
[X(t)] + N(t)
Eq. 2
X and N are two zero-mean stochastic processes jointly gaussian stationnary and ergodic in the wide sense. F is a linear transformation representing transport and deformation of structures within the jet. N is an additive independant noise, representing coming out or vanishing structures.
PRESSURE SENSOR
Eq.4
b
Eq.5
f denotes the frequency. ~ and GI are real and imaginary part of G(f) respectively. T is the integration time, Sxx( f) the power spect rum of X, C( f)\ the modulus of the coherence function of X and Y.
I
EXPERIMENTAL RESULTS Experiments were conducted with following conditions : - speed : 2 m/s to 8 m/s - fiber consistency : 1 g/l to 15 g/l - thickness of the jet : 10 mm to 20 mm
OPTICAL SENSOR + CORRELATOR / y / X
H
L=1m
VALVE
~.
FLOWMETER
Diagram of the experimental device
Ph. Bolon, E. Moisan and J. Sa ba ter
46
In order to compare the correla tion method with other conven tional instrum ents (electr omagnet ic flowme ter, impact pressu re sensor .•• ) we used an experim ental device built up at the Centre Techniq ue du Papier (Greno ble). The appara tus compri ses a vat having constan t level, an electro magne tic flowme ter, a flow regula ting valve, a pipe of square section . The outlet is compose d of a taper whose geometry can be varied (fig.4) . Apart from its width, the jet is identic al with those obtaine d on indust rial paperm achines, as far as speed, thickn ess, fiber consistenc y are concern ed. In order to rule out the effects of finite width, all measure ments were perform ed in the middle of the jet (in the cross-m otion directi on).
We have, in fig. 5
AQ
Qo
=
6.95 % and
Av Vo
7.05 %
Since it is diffi c ult to obtain a perfec tly steady flow rate, we may say that there is a good agreem ent between the two determ ination s. If we examine the fluctua tions of the measured veloci ty, we remark that the estima tion errors are compri sed within the limits ± 1.1 % Fig. 6 presen ts a simila r experim ent conduc ted in other condit ions. L
VELOCITY
Compar ison with an electro magne tic flowme ter. By varying the positio n of the flow regula ting valve, we genera te fluctua tions in the flowrate which are measure d by an electro magne tic flowme ter. These variati ons are compare d with those measure d by means of the optica l sensor . Fig. 5 shows the evoluti on of the flowra te and of the measure d veloci ty as a functio n of the time. Let 4Q and 4v be the variati ons of the flowrat e and of the veloci ty respec tively. Since the perpen dicular section in the flowmeter and in the pulp jet are di fferea t, we will examine the relativ e variati ons ~ and
I~
R
FLOWRATE
Qo
AV
-"
Vo 1 I
t ··
I I ·I
I·T T
1---+'-.,,- -
.. •
.• .
~~
.- ~ ~
. :T
F1g. 6. Compar 1son flowrat e - veloci ty Experim ental conditi ons : 5 .7 m/ s - jet spe ed - pulp comp osition : 70 % softwoo d, 30 % hardwo od - consist ency : 1 g/ l distanc e D : 6 mm - Correla tor using 4-bit quanti zation Averag ing time 64 ms The relativ e variat i ons are : .
,~
,
1----·-· -,-- . ---'---:---:----
AQ Qo
=
7.3 %
and
AV=7 . 2% Vo
,
Fig . 5 . Compar is on flowra te - veloci ty Experim ental conditi ons : 4.9 m/ s - jet speed - pulp compos ition : 60 % softwoo d, 40 %hardwoo d - consist ency : 10 g/ l - distanc e D : 5 mm - Correl ator uSing I-bit quanti zation Averag ing time 100 ms
The estima tions errors are larger (± 2.4 %) than in the previ ous case. This is caused by the short integra tion time (64 ms instead of 100 ms) and by the low consist ency. As a matter of fact, the state of floccu lation is a functio n of the fiber concen tration and a low floccu lation rate induces a poor correla tion between backsc attered signals X and Y. However, we should notice that this consist enc y is unusua l on paperm achines .
Jet Speed Measurement Influence of the distance between laser spots We know [11] that, because of shear stresses, large floes tend to be present at the center of the flow, where velocity gradient and turbulence intensity are minimum, whereas smaller ones are near the edges. Because of the mean velocity profile (in the z-direction), small floes move more slowly thna larger ones. For reasons of penetration of the laser beam, the measured velocity is less than the speed at the center of the jet. However, this drawback disappears if we increase the distance between laser spots D. As a mat ter of fact, the mechanical resistance of small floes is less than the one of large floes. Therefore, for large distances D, only large floes give a contribution to the correlation peak. Then, the velocity at the center of the flow can be measured by this method, with a sufficient precision. Fig. 7 shows the measured velocity vs distance D. The experimental conditions were : - jet speed - consistency - thickness of the jet
47 U(t)
Let :
=
Uo + u
Eq.7
where Uo is the mean velocity and u the turbulence term. We have P(t)
1" '2 \ (U o2 + 2uU o + u 2 )
Hence the mean pressure is :
oi
where is the variance of u and I the turbulence intensity. Because of the fibers, the turbulence intensity is low [5]. Then the corrective term can be neglected and the mean pressure yields a direct measurement of the jet veloci ty. Fig. 8 shows a comparison between results obtained with the optical sensor and wi th the pressure sensor.
8 m/s 8.8 g/l 13 mm
VELOCI TT
SO
VELOC ITY : M/S
7.5
PRESSURE SENSOf ""-{ -V::--; -=-_ ,J ( MI5)
J1J--(r :P;;"~~ENSO~ 1
.40
DI STANCE
1'. 10
7.0
~.
T.
DISTANCE D:MM I
5 ~.
10
•
.
(MM)
20
Comparison optical sensor - pressure sensor
Experimental conditions
I
15
20
Influence of the distance D
The shape of this curve is fairly typical. The importance of the transient zone (small distances) depends on the "roundness" of the mean velocity profile in the z-direction. Comparison with a pressure sensor. A pressure sensor is placed in the circuit as indicated in Fig. 4. It provides an electrical signal proportional to the total impact pressure. In a zone where static pressure is identical with atmospheric pressure, the instantaneous impact pressure is : Eq.6 where
Eq.8
U(t) is the instantaneous velocity ~ is the mass per unit volume of the fluid.
- jet speed : 5.5 m/s - thickness of the jet : 20 mm - pulp composition : 60 % softwood, 40 % hardwood - consistency : 10 g/l The correlation functions were computed over a large integration time (T = 15 s), so that the estimation error on the transit time can be reduced to 1 sampling period. In those conditions, the precision of the velocity estimation was ~.
.. DO
The velocity measured by means of the pressure sensor is Vp = 5.494 m/so If we examine Fig. 8, we remark the typical shape of the curve velocity vs distance D. But if we consider the results obtained with distances larger than or equal to 10 mm, we notice that the agreement between the two determinations is better than .5 % ! If we compute the mean value of the results obtained with the five largest distances, we obtain Vm = 5.484 m/so The agreement is better than .2 %.
48
Ph. Bolon, E. Moisan and J. Sabater
Discussion. The quality of the paper sheet depends on the flocculation, and especially on large flocs. This is one of the reasons why it is interesting to measure the- speed of these structures. Since the optical sensor uses backscattered light rather than transmitted light, it is sensitive to external phenomena. However, we saw that it was possible to access to the speed of the internal phenomena by increasing the distance between the laser spots. The reason why this speed measurement method works is that the velocity profile is rather flat in the z-direction. Even if the penetration of the laser beam is low, structures moving at maximum velocity are illuminated. Fig. 9 shows such a velocity profile, obtained bv means of a Pitot tube. VE!..OC I TY (M IS)
8,5
,"/--
•
8, 0
'-'-1' -'-.-.'-.. t I
Therefore, speed and ditions of cision of second.
is becomes possible to measure jet velocity fluctuations in the conan industrial machine with a pre1 % and with 10 measurements per
APPL I CATI ONS •
The speed measurement mehtod presented here was tested on different industrial papermachines. Fig. 10 shows a cross-correlation function obtained with the optical sensor on an industrial pul ~ jet.
31
u. ,
~I u. ,
1,5
Results presented in Fig. 5 and Fig. 6 seem to prove that a precision of 1 % can be approached with an integration time T = 100 ms. However, results are better than they seem to be, because the true velocity is itself slightly unstable. This unstability was pointed out by studying the instantaneous impact pressure. By filtering the pressure signal in the frequency band 0-5 Hz, we rule out the most part of fluctuations caused by the turbulence. In those conditions, signal fluctuat ions are of the order of 2.4 %. Since the precision of the sensor is 0.5 %, the velocity unstability is estimated to be about 1 %. This unstability is probably due to the design of the hydraulic circuit.
~I
e-'
~ I,
-(
,
'
J
-5
~.
,
I
z- 0 iRECTlOIIJ -
o
.5
J
,
'
,
,
J
POSITION (MM) Velocity profile in z-direction
Experimental conditions : - jet speed : 8 m/s - thickness of the jet : 13 mm - pulp : Bleached Kraft - consistency: 0.15 g/l
.. Fig. 10. Example of cross-correlation function
Similar curves were obtained in different conditions of speed and thickness. We notice in Fig. 9 that in a zone covering 8 cm in zdirection, speed variations are less than 1 %. With usual consistencies, fibers and flocs tend to be opposed to the velocity gradient [11), and then they increase the flatness of the velocity profile. These arguments show that the optical sensor can be used for measuring the absolute value of the jet speed in industrial conditions. If we are interested in tracking velocity fluctuations (for production optimization for instance), we need a given relative precision, say 1 %, with an integration time as short as possible. In these conditions, good results are obtained with large signal bandwidths and high correlation coefficients. As a matter of fact, if the consistency increases, flocs become largecand more resistant. Therefore, the signal bandwidth decreases and the correlation coefficient increases. It seems that the latter effect get the better of the other.
The correlation function is computed in the range 256 512 At, where 4t is the sampling period. The distance between laser spots is 19 mm and the jet speed is 640 m/min. We notice that the correlation peak is rather blunt, compared wi th sharpness of peaks obtained on papersheets [7).
4t -
Wi th this optical sensor, it is easy to determine the cross-motion velocity profile of the pulp jet. The support of the sensor is installed on a guiding rail (see Fig .12). It can be moved above the jet in both forward and cross-machine directions. There is no contact and the production is not disturbed. Fig. 11 shows a cross-motion velocity profile obtained in these conditions. The smooth curve (dotted line) is a parabolic regression. We notice that this machine presents a slightly asymetric profile. The fluctuations around the regression curve are caused either by the adjustment of the distance between the slices or by the hydraulic circuit up-stream of the slices.
Jet Speed Measurement
JET VELOCITr
CROSS-MOTION DIRECTION --
Fig. 11. Cross motion velocity profile on an industrial papermachine.
Fig. 12. Jet Speed Measurement on an Industrial Papermachine
49
Ph. Bolon, E. Moisan and J. Sabater
50
CONCLUSION Based on the cross-correlation of backscattered optical signals, the method proposed in the paper (correlation method) allows the jet speed to be measured without any contact. Experiments conducted at the Centre Technique du Paper and on papermachines show that, under the conditions of industrial production, speed measurement can be performed with a precision of the order of 1 %. The bandpass of such a velocimeter is large enough, so that it can be introduced in control systems driving the machine speed. The determination of the cross-motion velocity profile is obviously impossible by means of total head measurements in the box. Besides, impact pressure measurements cannot be carried out without disturbing the production. Then, the correlation method is an attractive solution to this problem, whose feasibility has been proven on different industrial papermachines.
[7] S. BAUDUIN, Ph. BOLON. A Paper Sheet Contactless Linear Speed Measurement. Proc. of 4th IFAC Conf. on Instrum. and Autom. in Paper, Rubber and Polymer Ind. (PRP4). Pergamon Press. Ghent. 3-5 June 1980. [8] G. SPIES, H. MEYR, J. BOHMANN. Real-Time Estimation of Moving Time Delay. Proc. of the IEEE Conf. ICASSP, Paris, 3-5 May 82. [9] 1. ANDERNO, A. SJOLUND. Laser Velocity Meter with Correlation Technique. Acta IMEKO, pp. 23-27, 1979. [10] Ph. BOLON, J .L. LACOUME. Speed Measurement by Cross-Correlation. Theoretical Aspects and Application in the Paper Industry. To be published in IEEE Trans. on Acoustics, Speech and Signal Proc., 1983. [11] G. DUFFY et al. making Fibers in BPBIF. Preprints Research Symp., Sept. 1977-.--
Hydrodynamics of PaperWater Suspension. Congo of the 6th Fundamental Oxford, Sess. 3, 18-23
- 0 -
ACKNOWLEDGEMENTS The authors wish to thank Messr Bauduin, Lafaverges and Palassof, of Centre Technique du Papier, for their active cooperation during this study.
REFERENCES [1] B. LEBEAU et al. Non Interacting Multivariable Papermachine Headbox Control Some Comparison with Classical Loops. Proc. of 4th IFAC Coni. on Instrum. and Autom. in Paper, Rubber and Polymer Ind. (PRP4). Pergamon Press. Ghent. 3-5 June 1980. [2] F.M. D'HULSTER et al. Application of Several Parameter - Adaptive Controllers to a Paper Machine Headbox. Proc. of 4th IFAC Conf. on Instrum. and Autom. in Paper, Rubber and Polymer Ind. (PRP4). Pergamon Press. Ghent. 3-5 June 1980. [3] L.C. LYNNWORTH. Clamp-on Ultrasonic Flowmeters ... Limations and Remedies. Instrumentation Technology, Sept. 75, pp. 37-44. [4] K.H. ONG, M.S. BECK. Slurry Flow Velocity Concentation and Particle Size Measurements using Flow Noise and Correlation Techniques. Measurements and Control. Vol. 8, Nov.1975. [5] Ph. BOLON, J. SABATER, S. BAUDUIN. A Contribution to the Study of the Stockjet as it leaves the Flowbox. To be published in Tappi Journal (1983). [6] T.S. DURRANI, C.A. GREATED. Laser Systems in Flow Measurement. Plenum Ed. 1979.