2012 International Conference on Fluid Dynamics and Thermodynamics Technologies (FDTT 2012)
IPCSIT vol.33(2012)©(2012) IACSIT Press, Singapore
Development of a Technique for Measuring Fiber Concentration
of Pulp Liquid Flow
Masaru Sumida 1+
1
Faculty of Engineering, Kinki University
Abstract. A light section method for evaluating the fiber concentration has been developed for flowing
pulp liquid. This method was applied to a fully developed steady flow in ducts with a square cross section.
The obtained results reveal quantitatively, in a definite form, the distribution of the fiber concentration, which
has long been an interesting subject of discussion among researchers. The effectiveness and applicability of
the present method are also shown. Furthermore, a discussion is given for the relationships of the
nonuniformity of the fiber concentration to the flow rate and the pressure loss. The pulp suspension flows in
ducts can be classified into five patterns, which are different from the previous classification.
Keywords: Pulp Liquid, Fiber-Concentration Measurements, Flow Pattern, Duct Flow
1. Introduction
Pulp suspension, a raw material of paper, is a liquid in which pulp fibers are suspended in water. This
liquid flows as an aggregation of pulp fibers, which repeatedly get to flock and disperse. Therefore, the fibers
in flowing pulp suspension are not distributed uniformly [1]. This brings about the possibility that paper of
irregular quality might be manufactured. For this reason, pulp suspension at the low concentration of 0.5 to
1.0% is used in current paper making machines. To save energy, it is necessary to make dehydration plants
more compact and also there is an urgent need for the development of technology that allows pulp fibers to
be dispersed uniformly in liquid at higher concentrations [2, 3]. However, an appropriate method of
evaluating the dispersion of pulp fibers has not been established yet. Consequently, a method of adequately
evaluating and analyzing the dynamic behavior of pulp fibers is greatly desired [1, 4, 5].
In this study, we consider the problems of pulp suspension flow in ducts with a square cross section. At
first, we develop an optical measuring method for evaluating the fiber concentration. Subsequently, we apply
this method to a fully developed steady flow. Furthermore, we discuss the variation of the uniformity of the
flowing fiber concentration with the flow rate.
2. Experimental apparatus
A schematic diagram of the experimental apparatus is shown in Fig. 1. The test ducts were made of
acrylic plates. The ducts were square and their sides, d, were 15 and 20 mm long. The pulp liquid flowing on
the horizontal plane including the duct axis was illuminated by a sheet of light of 1mm thickness from two
metal halide lamps (150 W). The illuminated plane was photographed from the upper side using a high-speed
camera (Photron FASTCAM-1024PCI) and a digital camera (Nikon D-100). The x and y axes of the
coordinate system are taken in the downstream and cross horizontal directions, respectively, as shown in Fig.
1. The working pulp liquid was a Kraft pulp (LBKP), which is the most commonly used pulp for paper of
high-quality at present. The raw material was made from broadleaf trees. The arithmetic mean and the
weighted mean lengths of the pulp fibers were 0.5 and 1.0 mm, respectively. The coarseness, given as the
mass per unit length of fiber, was 0.072 mg/m.
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
+
Corresponding author. Tel.: +81-82-434-7000; fax: +81-82-434-7011
E-mail address: sumida@hiro.kindai.ac.jp
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Fig. 1: Schematic diagram of
experimental apparatus.
The experiments were performed under the pulp concentrations of CS = 0.2 − 5%. These range from CS =
1% or less used in current paper-making machines to higher concentrations are executed to be used in the
future.
3. Method of evaluating fiber concentration in pulp liquid
In this section, we describe the method of evaluating the fiber concentration from the photographic
images taken in the plane illuminated by slits of light. The light irradiated from the lamps attenuates owing to
scattering and absorption by the pulp fibers. The attenuation characteristics in the direction of the duct width
were first determined with the pulp liquid sufficiently stirred in the calibration duct. The irregular source of
light included in the observed and photographic images was removed using the correction image with the
attenuation characteristics [6]. The images obtained in this manner were used to evaluate the fiber
concentration. Subsequently, the distributions of luminance were analyzed from the evaluation images.
Using the relation between the luminance and the fiber concentration established beforehand, the luminance
values were converted into concentrations using the following procedure.
First, we write I (x, y) for the distribution of the luminance of the evaluation image and let C (x, y) be the
corresponding distribution of the fiber concentration. Figure 2 shows the relation between the mean
luminance IA and the concentration CS of the pulp liquid. Here, IA is the value of local luminance I (x, y)
spatially averaged over the control surface A, i.e., the x-y plane. The calibration experiment was performed
for several strengths of the light source. An example of the case in which IA is divided by the value of IA, 0.6 at
CS= 0.6% is illustrated in Fig. 2. From Fig. 2, it is clarified that the relation between IA and CS can be
expressed, regardless of the strength of the light source, by the following simple empirical equation:
CS /CS, 0.6 ≅a(IA / IA, 0.6 )2 + (1−a) (a=0.95) .
(1)
Here, the strength of the light source in the present measuring system corresponds to the value of IA, 0.6.
Assuming that the above expression is applicable for the relation between I (x, y) and C (x, y) at a certain
point (x, y), we set
C (x, y) /CS =a{I (x, y) / IS}2 + (1−a),
(2)
where IS is the luminance value corresponding to the concentration CS of the pulp liquid.
The nonuniformity of the fiber concentration can be represented by Crms, which is the standard deviation
of the distribution C (x, y) of the fiber concentration over the control surface A. That is,
∫
Crms = ⎧⎨ (C − Cs ) 2 dA
⎩
Fig. 2: Calibration curve showing the
relationship between average
brightness and pulp concentration
(CS = 0.6%).
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∫
1/ 2
dA⎫⎬
⎭
.
(3)
Then, we estimate the value of Crms by using the values of IA and Irms for the luminance of the evaluation
image and by identifying the IS value in Eq. (2). It is assumed that the concentration CA averaged over the
control surface A including the axis of the straight duct is equivalent to CS, i.e., CA=CS, namely
1
A
∫ [a{I ( x, y) I
A
S
}2 + (1 − a) ]dA = 1
(4)
We rewrite I (x, y) in the above equation as I (x, y)=IA + Δ I (x, y) , and rearranging, we obtain the
relationship
IS = (IA2 + Irms2)1/2 .
(5)
Thus, we can easily estimate the concentration distribution C (x, y) using Eqs. (2) and (5) from the luminance
I (x, y) of the image.
When the variation of the luminance value, Δ I⁄IA, is small, the local concentration C (x, y) can be
expressed explicitly and obtained more simply as follows. For 0.2≥Irms/IA, we can write IS =IA with an
accuracy within 2%. Consequently, the degree of nonuniformity of the fiber concentration, β, can be
calculated as β=Crms/CS ≅ 2 Irms/IA . Moreover, the local concentration C (x, y) can be obtained in a similar
manner by substituting C (x, y) into C (x, y)=CS + ΔC (x, y). That is, from the preliminary measurement, the
relationship between IA and CS is approximately expressed as
IA ≅ k0 ⋅CSn ,
(6)
where k0 is a constant related to the visualization and measurement system. In particular, it depends on the
strength of the light source. In this analysis, it is assumed that Eq. (6) is applicable for the relation between I
and C at a certain point. Thus, we can associate ΔC with ΔI as
ΔC (x, y)/CS ≅ (1/n)⋅ΔI (x, y)/IS.
(7)
From the above, if the value of n is determined beforehand, the distribution of C can be readily obtained
from the I distribution of the evaluated images. The value of n is about 0.5.
4. Results and discussion
4.1. Understanding of pulp-fiber dispersion
To understand the behavior of pulp fibers, it is essential to examine beforehand the size of the area
element for which the local concentration in the pulp liquid can be defined. Moreover, it is necessary to
Flow
(a) Distribution of fiber concentration.
(b) Four-level distribution of
Fiber concentration
Fig. 3: Effect of area-element size on the local
concentration [Cs = 0.6%, Ua = 0.063 m/s,
y/(d/2) = 0.8]. (a) Lr = 0.004, (b) Lr = 0.02,
(c) Lr = 0.06, (d) Lr = 0.2
Fig. 4: Example of the distribution of fiber
concentration (Cs = 0.8%, Ua = 0.075 m/s).
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consider the fiber concentration at which the fibers can be assumed to be a mass in the flowing pulp liquid,
i.e., the concentration resulting in the flocculation of the suspension. However, unfortunately, neither matter
is referred to even in reports concerning current papermaking technology [4] or in previous works [1, 3, 5,
7−9].
First of all, it is important to establish the size of the area element from the viewpoint of measuring the
flow field. Figure 3 shows typical examples of changes in local concentration with time. Here, the
concentrations are obtained for various area-element sizes, Δy2, where Lr is the ratio, Δy⁄d, of the element
length Δy to the channel width d. From Fig. 3, it can be considered that the local concentration of pulp liquid
is suitably determined when Lr≈0.02. The ratio Lr should be in the range where there is no difference in the
value C’ of concentration fluctuation and where a noise with high-frequency components does not
significantly affect C’. Furthermore, the length Δy corresponds to the arithmetic mean length of the pulp
fibers, and the area-element size is equivalent to 6 × 6 pixels in the photographic images. Therefore, we
hereafter calculate the local concentration using an element size of Lr=0.02−0.03.
Figure 4 shows an example of the concentration distribution measured in the above-mentioned manner.
In Fig. 4, lighter regions correspond to a higher concentration of fibers. In addition, the light-and-shade bar
attached to Fig. 4(a) indicates the fiber concentration, i.e., C=0.4−1.2%. Nevertheless, it is convenient to
divide the image into regions with suitable concentration levels to further investigate the relation between the
flow characteristics and the nonuniformity of the fiber concentration in the pulp liquid.
In current papermaking machines, the nonuniformity of the fiber concentration is a problem, as already
mentioned in the introduction. However, the concentration nonuniformity has so far only been qualitatively
described on the basis of the light and shade of observation images [7−10]. Therefore, a quantitative
evaluation of a control surface has not been made [4, 10].
From such a viewpoint, we propose dividing the concentration distribution into four levels on the basis
of the values of both CS and Crms, which is the standard deviation of the distribution C (x, y) over the control
surface. We divide the concentration distribution as follows.
(i) C ≥CS + Crms; high-concentration region
(ii) CS + Crms ≥C ≥CS ; moderately high concentration region
(iii) CS ≥C ≥CS − Crms; moderately low concentration region
(iv) CS − Crms ≥C; low-concentration region.
The result of dividing the distribution in Fig. 4(a) into these regions is displayed in Fig. 4(b). For
convenience, we regard region (i) as where the flocculation of the suspension occurs. This region is assumed
to consist of areas of higher concentration, such as masses of fibers, while the pulp liquid is flowing.
(a) Pattern I (Ua = 0.025 m/s)
(d) Pattern IV (Ua = 0.38 m/s)
(b) Pattern II (Ua = 0.075 m/s)
0.2
(c) Pattern III (Ua = 0.20 m/s)
0.4% 0.6
1.0
(e) Pattern%V (Ua = 3.5m/s)
0.6
0.8
Fig. 5: Effect of mean velocity on the distribution of fiber
concentration (Cs = 0.6%). Left and right figures
show the distributions and four-level distributions
of fiber concentration, respectively. The pulp
suspension flows in the right direction.
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Flow
(a)
(b)
(c)
(d)
(e)
Fig. 6: Schematic diagrams of typical flow patterns of pulp liquid. (a) Pattern I: Plug flow with strong interaction
between fibers and duct wall, (b) Pattern II: Plug flow with hydrodynamic shear and fiber-wall interaction, (c) Pattern
III: Plug flow with water annulus in laminar shear, (d) Pattern IV: Mixed flow with fiber/water annulus and transitional
flow from laminar to turbulent, (e) Pattern V: Turbulent flow with distributed pulp fibers.
Fig. 7: Pressure losses for several concentrations of pulp liquid.
Fig. 8: Relationship between flow regime and pressure loss curve illustrated logarithm-mically as a function
of velocity.
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4.2. Pulp-fiber flow patterns
The changes in the concentration distribution with the flow rate are demonstrated in Fig. 5, where
CS=0.6% for the tested pulp liquid. The four-level distributions on the right of Fig. 5 are formed with
reference to the value of Crms for the low mean velocity Ua=0.025 m/s. The patterns of pulp-fiber
concentration in the flow can be classified into five types, patterns I−V, as illustrated in Fig. 6. A schematic
profile of the velocity is attached to each pattern. The previous classification method is based on the relation
between the pressure loss and the flow rate [11, 12], where the flow characteristics are classified into
three reference to the value of Crms for the low mean velocity Ua=0.025 m/s. The patterns of pulp-fiber
concentration in the flow can be classified into five types, patterns I−V, as illustrated in Fig. 6. A schematic
profile of the velocity is attached to each pattern. The previous classification method is based on the relation
between the pressure loss and the flow rate [11, 12], where the flow characteristics are classified into three
types: (i) plug flow, (ii) mixed flow, and (iii) turbulent flow. The relation between the pressure loss per unit
length, ΔP/L, and the mean velocity in our experiment is shown in Fig. 7 for the duct of d=20 mm. The solid
lines in Fig. 7 indicate the results for water. Moreover, the correspondence of the ΔP/L−Ua curve in Fig. 7
with patterns I −V is shown in Fig. 8. As the pulp-liquid concentration CS increases, the mean velocity at
which the pattern shifts to the next one becomes larger. Referring to the previous classification [11, 12],
patterns I and II correspond to plug flow, patterns III and IV are equivalent to mixed flow, and pattern V
corresponds to turbulent flow.
5. Conclusions
A light-section method is developed to clarify the distribution of the fiber concentration in flowing pulp
liquid. The characteristics of the flow in ducts are also investigated. The principal achievements and findings
of this study are summarized as follows.
(1) The present method was proved to be effective and extremely convenient for evaluating the distribution
of the fiber concentration of pulp liquid, regardless of the strength of the light source, in the case of a
moderate concentration of less than about 1.0%.
(2) The flow of pulp liquid in a duct is classified into five patterns according to the flow mechanism and the
characteristics of the fiber-concentration distribution. This classification is different from the previous
classification of flows, that is, into plug, mixed, and turbulent flows.
6. Acknowledgements
The author would like to thank Mr. S. Suzuki of Metso Paper Japan Co., Ltd., and Mr. T. Fujimoto of
MHI Solution Technologies Co., Ltd., for helpful discussions. Mr. K. Kazuhiro of Oji Paper Co., Ltd.,
assisted this investigation by supplying the pulp liquid. This work was supported in part by MEXT
KAKENHI (23560212).
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