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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: [email protected] 118 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%). 119 ∫ 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). 120 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. 121 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. 122 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. 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