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THEORETICAL BACKGROUND OF NEW ENERGY SAVING REFINER SEGMENTS DESIGN
ABSTRACT The flow field in a refiner is very complex, due to the fact that it involves multiphase, nonNewtonian fluid flow. For that reason, the design of refiners has been mainly based on experiments. This paper presents results of the work conducted in highconsistency thermomechanical pulp (TMP) refiners, used in mechanical pulp manufacture, for topquality coated papers. A design method for refiner segments is presented, with which the effect of different geometrical parameters on energy consumption and pulp quality can be studied. The basic idea is to apply the theory of impeller pumps to design the geometry of refiner segments, and determine their effect on the flow field. In addition, to make the refiner to work as a proper flow machine, strong acceleration and deceleration of flow must be avoided. With regard to the pulp quality, the numerical model of nonNewtonian flow in grooves provides some general trends. The theoretical approach has been verified by trials in refiner mechanical pulping mills. Measured and calculated temperature distributions of refiner segments correlate favorably. It was also observed that the energy consumption of the refiner with newly designed segments was clearly reduced compared with traditional segments, and the pulp still fulfilled the quality requirements. INTRODUCTION In many papers, the high specificenergy requirement for mechanical pulping and especially refining of mechanical pulps has been discussed. The electrical energy can account for more than 35 % of the total cost of manufacturing TMP. The exact figure depends on the local conditions but generally the electricity cost is the second largest cost item after wood raw material for a TMP mill. The importance of the electricity cost is even more significant now when markets facilitate real time pricing for electricity, which has made the price of electricity highly volatile. Härkönen and Tienvieri reviewed a number of ways to reduce energy consumption ranging from chip treatment to new segment geometries [1]. As noted in an earlier report [2], the development has focused recently on reducing the energy consumption by developing processes based on high pressure and high temperature [3,4]. Unfortunately, the high temperature in the disc gap is detrimental to the brightness of the pulp [5]. It has also been shown that with changes in refiner segment design, it is possible to achieve savings in refiner energy consumption when refining spruce fibers, but very little has been published regarding the effective refining of hardwoods [6]. Härkönen and Tienvieri concluded their paper by calling for a new approach, in which the discgap phenomena would be treated more scientifically [1]. In the study below, the refiner is considered as a hydraulic machine, where complex flow and heat transfer are combined with very delicate wood fiber processing to produce pulp of a certain required quality. It is therefore extremely important to understand the flow conditions inside the refiner to control the process and to produce the required type pulp. Many different types of approaches have been tested earlier, and several articles are published in the literature, but no satisfactory results have appeared on the subject. Perhaps the bestknown basic article to describe the refining is that by Atack et al. [7] in 1984. Even before that, Miles et al. [8] wrote a report on the flow conditions inside a refiner . Taking advantage of porous media approximation, they described steam flow through a porous fiber network. Later, this work was continued by describing the flow of a pulp phase inside the refiner [9]. Some other reports, e.g., by Allison et al. [10], were written on the subject, starting from a new, revised basis. Still no clear ideas have been presented to obtain detailed information about the flow inside the refiner, and to understand the effect of flow on energy consumption or pulp quality. Furthermore, some descriptions have appeared in the literature about the effects on the refining process of different operating parameters, such as production rate [1], rotational speed of the refiner [11], chemical addition [12], and variation of operating parameters [13]. Moreover, some attempts have been made to find a connection between the operating parameters and pulp quality [14], [15] and to simulate the interrelationship [16]. A numerical program was also developed to simulate the flow situation inside the refiner [17], and a couple of reports have appeared on experiments on the refining process to measure residence time [18, 19], velocities [20], and power consumption distribution [21] inside the refiner. In the present study, a totally new approach was adopted, based on the real physical behavior of particle suspensions and flow conditions inside the refiner. The flow situation was divided into two levels of approximation: 1) the main flow in the radial direction of the refiner along the grooves, and 2) a secondary flow inside the refiner grooves and between bars in the angular direction. The main flow characteristics determine the gross features and the functionality of the refiner, while the secondary flow characteristics determine the refiner's pulp quality parameters. The above approach can be applied basically to any refiner, but the results below are only for the firststage singledisc and CD (conical disc) refiners. THEORETICAL BACKGROUND Typically, TMP refiners operate with disc gaps between 0.52.0mm. Refiner segments in each refining position are tailored to fulfill local requirements for operational stability, pulp quality, and energy consumption. Wood chips with certain moisture content are fed into the eye of the refiner by feed screw and diluted with water. The center section crushes and fiberizes the chips, while the outer and fine sections refine the fibers and give quality to the pulp. The process involves high shearing and deforming of the material and therefore consumes considerable amounts of energy. The high power consumption again produces heat, which vaporizes the dilution water and some water from the wood chips, turning the waterchip suspension fed into the refiner into a fibersteam suspension at the end of the process. This increases the complexity of the problem because the processed material now differs completely from what it was at the inlet into the refiner. Consequently, the problem has to be analyzed in a versatile manner, whereby we must exploit various aspects of fluid dynamics: nonNewtonian fluid dynamics, multiphase flow dynamics, and heat transfer. In analyzing pulp quality parameters, we can also resort to some statistical analytical methods because of the analogy between the refining and mixing processes. Fig 1. The schematic presentation of refiner segment design procedure Fig 2. The schematic presentation of pump design procedure
Analysis of the refiner flow consists of four distinct approaches: pump design theories to design the desired refiner geometry; main flow field analysis, with a 1D computer program based on reduced set of NavierStokes equations with continuity and energy equations; 2.5D numerical simulations, where a certain flow rate is introduced through 2D computational domain to analyze the secondary flow field; and mixing analysis to predict pulp quality parameters. Pump design theory: The disctype refiner can be considered a type of hydraulic machine, similar to the centrifugal pump. Pump design theory was therefore adopted for refiner analysis to obtain the benefits of optimally designed geometry and optimal pumping angles and to reduce power consumption in the refiner. The optimal geometry here resembles that of the centrifugal turbo fan, because the main flow medium inside the refiner is steam. Yet we cannot ignore the effects of wood fibers, which we must take into account in the material parameters of the flowing medium. n this study, the Eulerian approach was applied, based on Euler's equations for pump design together with the familiar model laws, which a turbo machine must obey to work properly [22 ]. The most important of these is the specific speed, because it determines the design of the pump or fan (axial or radial design, 2 or 3D blades, etc.). All the other parameters should somehow relate to each other for a working concept. (A more comprehensive view of pump design theory can be found in the literature [22, 23].) Mainflow field analysis: Analysis of the main flow field and the gross features of the refiner flow was based on the reduced set of NavierStokes equations together with continuity and energy equations in cylindrical coordinates. The full set of equations is presented in Appendix A (see equations (1), (2) and (3)), and the reduced set may be derived from the equations by opening them and writing them for a steady state situation for incompressible fluid without body forces. Fig 3. The schematic presentation of 1D computer program design procedure In the case of a refiner where the angular velocity component dominates, the gap between the discs is very narrow (usually < 1mm in the outer periphery), and the apparent viscosity of the fibersteam suspension is very high because of a high solid content of fibers (~ 4050%), the set of equations is reduced to a simple 1D set of equations. The final form of the set of equations depends on the material function that is used to determine the shear stress in the flow channel. For example, if we use the simplest nonNewtonian fluid model, the Powerlaw model (9), we get the pressure (12) and temperature (13) profiles in the radial direction (see appendix). Based on the set of equations, a 1D computer program was developed to simulate the main flow features inside the refiner in the radial direction. These calculations yielded the pressure and temperature profiles in the radial direction. Furthermore, it was possible to define the relation between the volumetric fractions of steam and fibers from the steam generation term. The phase change of water also modifies the material parameters of the suspension, which, therefore, had to be updated continuously during calculation. In fact, the phase change term closed the set of equations, and the entire computation procedure involved numerous iterations between these equations. Secondary flow field analysis: To understand the overall flow situation inside the refiner, we must analyze the secondary flow field inside the refiner grooves and between bars. Since the flow field in the refiner is not 1D, as approximated in the main flow analysis, but a very complex 3D field, a 2.5D numerical model was constructed. The situation is quite different on the rotor and stator sides: the rotor side shows a centrifugal force component, while on the stator side the component is absent, and the flow field is controlled solely by pressure and friction forces. Therefore, the rotor and stator sides can easily be simulated separately and the results combined afterwards for a complete refiner model. The commercial numerical Polyflow code was used for simulation. It is a finiteelementmethodbased program with a large material function library and with a capability to handle 2.5D flow situations, in which the main flow field flows through a 2D geometry. Pulp quality prediction: The refining process resembles a mixing process, because both aim to produce as homogeneous a suspension or mixture as possible. During processing, the material is stressed and strained, and the resulting substance is a function of the history of deformation along the flow field. This is why mixing theory was adopted to analyze the quality of the pulp. One way to measure the mixing in a flow situation is to calculate the stretching of infinitesimal vectors attached to the material points dispersed in the flow domain. As the points move in the flow field, the vectors are stretched. The stretching and the rate of stretching of these vectors are the interesting properties, because they vary from point to point in the flow domain and evolve with time [24]. Mixing can also be numerically observed by assigning a number of material points, with an initial orientation, to an earlier computed flow field. When the material points are tracked as a function of time, successive values of mixing parameters are being calculated. When the material points are numerous enough, for example 1,000, they are independent and calculated quantities can be treated statistically. On the basis of this theory, a relation can be established between the deformation history of the fluid and such pulp quality parameters as tear and tensile strength and fiber length. (More about the mixing theory can be found in the literature [25].) EXPERIMENTAL VERIFICATION Measurements in the refiner studies can be divided into two distinct types: flow measurements to analyze the flow situation inside the refiner and pulp quality tests to analyze the refiner's refining capability and the quality of the pulp produced. Both measurements are important in understanding the physical conditions in which refining occurs and the process of producing certain quality pulp for a specific paper grade. In this study, very special instrumentation was built inside the refiner to analyze its thermodynamic conditions: 16 thermocouples were mounted in different radial positions on the stator disc to obtain a radial temperature distribution. When saturation temperature was assumed in the refiner, the radial pressure distribution inside the refiner could be determined from temperature measurements. Initially, the refiner segment design theories developed were verified in the Mreal Kirkniemi mill where spruce TMP is produced for use in lowbasisweight, filmcoated LWC paper. These studies showed that it is possible to change the basics of the refining process. Fibers and steam flowed through the refiner in a controlled manner and all the backflow was minimized. With the new refiner segments the energy consumption in the main refining line was reduced by up to 30%. The refiners in Kirkniemi are of the flat singledisc, Metso Paper RGP268 refiner units. The TMP line has no preheating stage and the production of the refiner line is 100 ADMT/D [2]. The effect of two different segments on the measured and simulated temperature distribution in the disc gap of the primary stage refiner is shown in Fig. 4. In the figure, new Turbine^{TM} segments are compared with earlier low energy (LE^{TM}) segments, which already reduce the refining energy compared with standard segments [6]. MReal started up an Aspen BCTMP mill in Joutseno in August 2001. The Joutseno mill is equipped with Metso's highcapacity refining system based on two parallel lines of twostage refining using RGP82CD mainline refiners. The total production of the mill is 800 ADMT/D of bleached pulp. The refiner design is important when using this type of approach for segment design. Previous developments made on flatdisc refiners equipped with feeding type segments often led to narrow disc gaps. The CD refiner has a large operating window due to the conical shape of the refining surface and new segment types can be tuned to optimized geometry while still maintaining a stable disc gap and producing pulp at a good quality level [2]. Fig. 4 Measured and simulated steam temperatures with low energy (LE) and Turbine Segments in primary stage RGP268 flat singledisc refiner when refining spruce.
After a short operating period, the refiner segments at Joutseno mill were changed to the new design, which was based on the theoretical approach. The new Turbine segments showed excellent results from the first trial and the mill changed all primary stage segments to the new types. Even though primary refining is done in an extremely aggressive manner, the large operating window has made it possible to maintain the primary refiner in a stable operating mode. Segment life does not differ from that of standard segments and 2000 hours represents a typical average segment life in the mill. The new segments for the RGP82CD refiner in the Joutseno mill are shown in Fig. 5. As shown, they differ greatly from the traditional refiner segments. With the new refiner segments design, the flow of steam is forced forward in the refiner and the pressure at the inlet of the primary stage refiner is close to atmospheric. This low pressure during the chip defibration stage improves the optical properties of the refined pulp. Measured and simulated temperature profiles for Turbine segments and standard segments are shown in Figure 6. It is evident that the new segments have resulted in reduced temperature in the feed zone and a decrease in the peak temperature in the conical disc gap . The CD refiner works with the new segments in such a way that the flat zone is used to increase the pressure without generating significant amounts of blowback steam. In the CD zone, the refining is carried out with a decreasing temperature profile indicating forward flow of both steam and pulp. Fig. 5 Turbine segments of Metso Paper's RGP82CD refiner. Fig. 6 Measured and simulated steam temperatures with Turbine Segments and standard segments in primary stage RGP82CD refiner when refining aspen. In the earlier report, the authors presented data for main line and disc filter pulp quality and specific energy development, with the primary refiner equipped with Turbine or standard segments and the secondary refiner with lowenergy (LE) segments [2]. During these test periods, the mill was producing pulp for LWC grade paper. The final properties of the pulp are then tuned in the bleaching stage. Pulp quality was evaluated in the R&D laboratory of Metso Paper in Sundsvall. Some optimization of the impregnation phase was carried out and this had a positive impact on pulp brightness. The raw material blend during these trials was 85 % aspen and 15 % spruce. Difference in time between presented trials may have caused variation in wood quality and therefore in quality results. One important feature was that the impregnation was carried out at very low caustic charge level and the specific energy consumption in the mill has thus been reduced by effective refining rather than as a result of caustic addition [2]. According to the data, the most striking effect of new segments was the reduction in refining energy, which represents a saving of more than 25% for the refining line itself and more than 20% for the total energy consumption for the mill. The increased brightness level of the pulp before the bleaching stage also reduces the consumption of bleaching chemicals required to achieve a given final brightness level. This reduction combined with the energy reduction has improved the overall production efficiency of the Joutseno mill very significantly. It should be noted that despite the lower energy consumption observed for the Turbine segments, the fibers have been developed to a similar degree with regard to strength properties. Furthermore, since the fiber length remained constant at 1.0 mm, this suggests that the refining treatment was not too harsh although the increased scattering coefficient indicated an increased degree of fiber wall development [2]. RESULTS AND DISCUSSION Main flow field: In the 1D simulation, boundary conditions were chosen to correspond to the true millscale refiners described above. As for the results, radial pressure and temperature distributions inside the refiners were computed from motion and energy equations, respectively. Simulated profiles agree with measured profiles, if the saturation condition is assumed to prevail everywhere inside the refiner. Both profiles are strong functions of the geometry. The radial pressure distribution is mainly determined by centrifugal and friction forces, and the angle of bars has a significant impact on the profile. The geometry also affects temperature distribution, because it determines the power consumption and thereby heat production inside the refiner. The steam flow rate and the feeding pressure are also strong functions of the geometry: the segments designed according to the pumping theory can convey steam at rates several times higher than traditional segments. This also influences the pressure and temperature profiles, since the volumetric fraction of steam determines the material parameters of the steamwaterfiber suspension and thus the ratio between the centrifugal and friction force. Figs. 7 and 8 show the profiles of power consumption distributions inside the refiners for different segment geometries, with different boundary conditions, respectively. Fig. 7 Simulated specificenergy consumption distributions with lowenergy (LE) and Turbine Segments in primary stage RGP268 flat singledisc refiner when refining spruce. Fig. 8 Simulated specificenergy consumption distributions with Turbine Segments and standard segments in primary stage RGP82CD refiner when refining aspen. Recently, articles have been published about measurements of power consumption distribution inside refiners. Gradin et al [21] used strain gauges on the bars to measure the straining between the bars in a disc refiner. Integrated or summed over the bar area, the straining gives the total power consumption distribution. Backlund et al used piezoelectric load sensors and thermocouples to measure tangential forces and temperature, respectively, in the flat zone of a CD refiner [26]. From measured tangential forces, local power consumption distribution can be calculated by multiplying the disc gap by the refining area. Both of the above results agreed with our 1D simulations. Secondary flow field: In the numerical simulations, the shear thinning behavior of steamwaterfiber suspensions were taken into account by employing the Powerlaw model, because shear thinning clearly affects the flow field inside the refiner grooves. The effect can be seen in the contour figures in Appendix B, where in 2D the contour of velocity component along the groove is shown for Newtonian fluid. The effects of a material's shear thinning are best seen in the fluid's effective area of relative movement on the stator side. With a Newtonian fluid, nearly the entire groove area is moving, whereas with a shear thinning fluid, the effective area is clearly reduced, and the value of the stream function is much lower than in the former. This is an important phenomenon when considering the mixing inside the groove. The particles on the bottom of the groove are retained there much longer than those on the top and will therefore be much less refined than other particles. Accordingly, the intensity distribution in refining is thus wider for a shear thinning fluid than for the Newtonian fluid. This feature must be kept in mind when designing bar and groove geometries of segments. The effects of shear thinning behavior also reflect on pressure and shear rate values between the bars, because shear thinning acts on the thrust force, which separates the rotor and stator discs and on the deformation sustained by fibers moving through the gap between the bars. The thrust force, produced by the relative movement of rotor to stator, is related to the geometry of the bars. The bar angle of incident is relevant: the smaller the angle, the higher the pressure peak on the edge of the bar and therefore the thrust force. But as the incident angle of bars becomes larger and the radial pressure profile inside the refiner becomes flatter, the net force separating the discs becomes negative, and the discs are drawn together. These thrust force results can be combined with results of the radial pressure distribution of the 1D model for the total force separating or attracting the refiner discs. In addition, the shear stress in the disc gap is also a strong function of the bar geometry and the disc gap itself. The value is not constant but has high peaks at bar edges. This feature should contribute to the strength of the produced pulp, because with smaller disc gaps the shear stress peaks on the outer rim may rise to several MPa's, becoming thereby larger than the internal strength of wood fibers and causing fibers to be cut. Pulp quality: The pulp quality analysis with mixing simulations showed clearly that bar and segment geometries affected the refining efficiency: with larger angles of incident, the radial pressure profile became flatter and recirculation decreased. This means that the intensity distribution of refining becomes narrower and the produced more homogeneous pulp. With radial bar geometry, such as in traditional segments, the force resultant acts on fibers by driving them into the bar gap and increasing power consumption, which produces more heat and steam, and radial temperature and pressure profiles become more parabolic. In addition, this process creates an adverse pressure gradient on the stator side and thus more backflow. Pulp quality now varies more and more because some fibers that flow along the rotor grooves pass very fast through the refiner and undergo only small deformations, while others that flow backward in the stator side remain longer in the refiner and undergo higher net deformation. Therefore, as flat a pressure profile as possible inside the refiner is desirable to produce homogenous pulp. The effects of the material's shear thinning are also pronounced in the results. With a decreasing shear index, mixing inside the grooves becomes weaker and refining intensity decreases. The intensity also begins to fluctuate because fibers in the bar gap undergo high deformations, while those on the bottom of the grooves remain there and emerge very raw, i .e., nondeformed (= unrefined). Therefore, we need dams in the rotor grooves to lift the material that is stuck there, especially for particle suspensions such as pulp, that exhibit non Newtonian, shearthinning behavior. On the stator side, dams are beneficial in the case of an adverse pressure gradient. Particle simulation results are shown in Appendix C, where refining intensity distribution is presented for zeropressure gradient flow situations. CONCLUSION In the paper, a theoretical framework has been presented for the new refiner segments design procedure to reduce energy costs in the mechanical pulping. The approach has been to change the basics of the refining process. The disc refiner has been considered as a type of hydraulic machine similar to a centrifugal pump. Pump design theory has therefore been adopted in the refiner analysis to obtain the benefits of optimally designed geometry and optimal pumping angles, and to reduce energy consumption in the refiner. Pulp quality and flow field in a refiner are closely interrelated. The flow field was analyzed with either inhouse 1D computer program for refiners or commercial numerical tools. Pulp quality parameters were studied by exploiting the mixing theory and using the commercial numerical code for laminar simulations, and by comparing the results to a millscale pulp quality test. A clear correlation was established between flow features and pulp quality parameters. The results obtained from this theoretical approach were then used as the starting point for refiner segment development. The new product series of refiner segments, i.e. Turbine^{TM} segments, was developed on the basis of the theoretical design procedure. The details on the subject will be found in the literature in a near future. In the Mreal Joutseno BCTMP mill, the refining energy savings obtained with the new refiner segment technology represent more than 20% of the total energy consumption of the mill. Increased brightness of the pulp before the bleaching stage also reduces the consumption of bleaching chemicals required to achieve a given brightness level. The combination of energy reduction and chemical savings has made a valuable contribution to the efficiency of the Joutseno operation and provides incentive for future development work on hardwood mechanical pulps. ACKNOWLEDGEMENTS The authors would like to thank the personnel from the Mreal Joutseno and the Mreal Kirkniemi mill for their work in supporting this millscale development project. They would also like to thank other members of the development group: Mr. Marko Pekkola of Mreal Joutseno Mill, Mr. Markku Leskelä and Mr. Olli Alhoniemi of Mreal Kirkniemi Mill, Mr. Nils Virving, Mr. Peter Bergquist and Mr. Olof Kjellqvist of Metso Paper for their diligence. The authors also thank Mr. Aarre Metsävirta of Mreal for the support, which made this development real, and Mr. Chris Hurst of Bugli Company for his help in preparing the manuscript. REFERENCES 1. Härkönen E., Tienvieri T.: The Influence of Production Rate on Refining in a Specific Refiner. Proceedings of 1995 International Mechanical Pulping Conference. Helsinki, Finland. 2. Vikman, K., Leskelä, M., Pekkola, M., Vuorio, P., Tyrväinen, J., Huhtanen, JP.: Proceedings of 2003 International Mechanical Pulping Conference, Quebec, Canada, pp. 9195. 3. Höglund H., Bäck R., Falk B., Jackson M.: Thermopulp^{TM} – A New Energy Efficient, Mechanical Pulping Process. International Mechanical Pulping Conference. Ottawa, Canada, 1215 June 1995, pp. 213225. 4. Sabourin M., Xu E., Musselman R.: Evaluation of Refiner Disc Speed, Plate Design and Consistency on High Pressure / Low Residence (RTS)TMP Pulps. International Mechanical Pulping Conference. Stockholm, Sweden, 913 June 1997, pp. 241249. 5. Koskinen J., Salerma M., Forsskahl I: HotShot: Rapid HeatAging of Mechanical Pulps. International Mechanical Pulping Conference. Stockholm, Sweden, 913 June 1997, pp 377379. 6. Bergquist P., Vuorio P.: New Refiner Segments Technology to Optimise Fiber Quality and Energy Consumption of Refiner Mechanical Pulp. Proceedings of 1995 International Mechanical Pulping Conference. Helsinki, Finland. 7. Atack, D., Stationwala, M. I., Karnis, A., What happens in refining. Pulp and Paper Canada, 85(12), pp. 119124, 1984. 8. Miles, K. B., Dana, H. R., May, W. D., The Flow of Steam in Chip Refiner. International Symposium on Fundamental Concept of Refining, Appleton, WI., pp. 3042, 1980. 9. Miles, K. B., May, W. D., The Flow of Pulp in Chip Refiner. Journal of Pulp and Paper Science, 19(6), pp. J63J72, 1990. 10. Allison, B. J., Isakson, A. J., Karlström, A., Greybox Identification of a TMP Refiner. Proceedings of 1995 International Mechanical Pulping Conference, pp. 119124, Helsinki, Finland. 11. Munster, H., Dahlqvist, G., Operational Experience with the First Commercial High Speed Refiner at Perlen Papier AG, Switzerland. Proceedings of 1995 International Mechanical Pulping Conference, pp. 197202, Helsinki, Finland. 12. Engstrand, P., Karlström, A., Nilsson, L., The Impact of Chemical Addition on Refining Parameters. Proceedings of 1995 International Mechanical Pulping Conference, pp. 281286, Helsinki, Finland. 13. Strand, B. C., The Effect of Refiner Variation on Pulp Quality. Proceedings of 1995 International Mechanical Pulping Conference, pp. 125130, Helsinki, Finland. 14. Stationwala, M. I., Mathieu, J., Karnis, A., On the Interaction of Wood and Mechanical Pulping Equipment. Part I: Fiber Development and Generation of Fines. Proceedings of 1995 International Mechanical Pulping Conference, pp. 157163, Helsinki, Finland. 15. Stationwala, M. I., Mathieu, J., Karnis, A., On the Interaction of Wood and Mechanical Pulping Equipment. Part II: Pulp Quality. Proceedings of 1995 International Mechanical Pulping Conference, pp. 165170, Helsinki, Finland. 16. Qian, X., Tessier, P., A Mechanistic Model for Predicting Pulp Properties from Refiner Operation Conditions. Tappi Journal, Vol. 78, No. 4, pp. 215222, 1995. 17. Härkönen E., Ruottu S., Ruottu A., Johansson O.: A Theoretical Model for a TMPRefiner. International Mechanical Pulping Conference. Stockholm, Sweden, 913 June 1997, pp. 95102. 18.Ouellet, D., Bennington, C. P. J., Senger, J. J., Borisoff, J. F., Martiskainen, J. M., Measurement of Pulp Residence Time in a High Consistency Refiner. Proceedings of 1995 International Mechanical Pulping Conference, pp. 171176, Helsinki, Finland. 19. Härkönen E., Huusari E., Raviala P.: Residence Time of Fiber in a Single Disc Refiner. International Mechanical Pulping Conference. Houston, TX, USA, 2426 May 1999, pp. 7786. 20. Alahautala T., Vattulainen J., Hernberg R.: Quantitive Visualisation of Pulp Refining in a Production Line Refiner. International Mechanical Pulping Conference. Houston, TX, USA, 24 26 May 1999, pp. 8795. 21.Gradin, P. A., Johanson, O., Berg, JE., Nyström, S., Measurement of the Power Distribution in a SingleDisc Refiner. Journal of Pulp and Paper Science, Vol. 25, No. 11, pp. 384387, 1999. 22.Pfleiderer, C., Die Kreiselpumpen fur Flussigkeiten und Gase. SpringerVerlag, Berlin, 1961. 23. Lazarkiewicz, S., Troskolanski, A. T., Impeller Pumps. Pergamon Press, Warszawa, 1965. 24. Ottino, J. M., The Kinematics of Mixing: Streching, Chaos and Transport. Cambridge, University Press, 1989. 25. ManasZloczower, I., Tamdor, Z., Mixing and Compounding of Polymers, Theory and Practice. Hanser/Gardner Publications, Inc., Cincinnati, 1994. 26.Backlund, HO., Höglund, H., Gradin, P., Study of Tangential Forces and Temperature Profiles in Commercial Refiners. Proceedings of 2003 International Mechanical Pulping Conference, Quebec, Canada, pp. 379386.
(We apologise for the quality of the image above and are trying to obtain a better reproduction of the equations from one of the authors, whose email address is petteri.vuorio@metso.com ) ) APPENDIX B Zvelocity component along grooves for Newtonian fluid.
APPENDIX C Particle simulation along grooves for Newtonian fluid: 