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Abstract： Disc refiner is a critical equipment in the pulping and papermaking industry， pulp is refined in the refining zone， and different bar structures of refining disc constitute the different refining zones. With the use of the 3D modeling software SOLIDWORKS， five different refining discs that are commonly used in low consistency pulping， were built. The five refining discs were simulated and analyzed using the Computational Fluid Dynamics （CFD） software. The distribution of pulp velocity and surface shear stress， which is displayed between the bar and groove structures， can indirectly show the stress conditions on the refining discs. This paper provides a theoretical basis for research on the bar and groove failure of the refining discs.
Keywords： pulping； disc refiner； bar structure； CFD
1 Introduction
Disc refiners have been widely used in the pulping and papermaking industry. The refining disc is a core component of a disc refiner. There have been extensive researches on refining discs including materials， manufacturing process， principles of the structure failure， arrangement of the bars and grooves， and energy consumption. The design and structure of a refining disc will directly affect the beating quality and energy efficiency of the disc refiner[1-4].
In recent years， Computational Fluid Dynamics （CFD） has become a decisive method for studying fluid motion and understanding flow regularity. Therefore， the CFD method has provided an efficient way of simulating and analyzing process fluid machinery. Research in CFD simulations on disc refiners of pulping process started late in China[5]. With the development of computer numerical simulation technology， the CFD method increasingly shows the advantages of studying the pulping process of the disc refiner.
Although the simulation of a macroscopic refining disc takes longer than that of a partial one， it can provide a realistic representation of the refining zone including the pulp velocity， stress condition， and the flow path. Using the 3D modeling software SOLIDWORKS and the CFD software Flow-simulation， five different macroscopic refining disc bar structures have been built and simulated under the same conditions.
2 Modeling
Differences between bar structure refining discs are roughly divided into five groups： Radiation Lines Straight Bars， Isometric Parallel Straight Bars， Isometric Parallel Straight Bars with Dam， “V” Type Bars， and Arc Bars. These five types of refining discs will be referred to from now on as DISC-1， DISC-2， DISC-3， DISC-4， DISC-5 shown in Fig.1. The five different bar structures of refining discs were built in SOLIDWORKS. Considering the complexity of the refining disc structure， particularity of the fluid， and the computational speed， the five refining discs were taper and bolt simplified. Furthermore， the discs were all simulated as flat bars to ensure the efficiency of the simulation progress. Table 1 shows the modeling parameters of the five refining discs.
3 Flow field settings
3.1 Basic settings
Initially we imported each pair of refining discs’ 3D model from SOLIDWORKS into Flow-simulation. We used Wizard to begin a setting procedure， selected the Internal flow in the Analysis type option， and selected Exclude Cavities Without Condition. In the Rotation option， we chose the geometric center of the disc as the rotation axis； finally we defined the surface roughness
（0 mm） and ignored the influence of the gravity.
3.2 Boundary conditions
Taking DISC-1 as an example （Fig.2） we set the boundary conditions in Flow-simulation are as follows.
（1） Inlet boundary conditions. The entrance is a circular cross section， flow rate is 0.01 m3/s.
（2） Outlet boundary conditions. We set the outer edge of refining zone as a free export （101325 Pa=1 atm）.
（3） Wall boundary conditions. We set the stator as a static， real wall （0 r/s in the coordinate system）. Furthermore， we set the rotor around the center axis of rotation （105 r/s）.
（4） Minimum gap. The minimum gap in the refining zone （gap between two discs） was set to 1 mm. Moreover， the results accuracy， 5-class， adaptive mesh technique of Flow-simulation， was set to automatically turn on.
It should be noted that there is no existing pulp fluid mathematical model in any CFD software as of yet. Researchers usually assumed the pulp as constant viscosity Newtonian fluid and analyzed it as such in CFD software. Results based on literatures[6-7] and simulations fit the experimental data properly. In this study we assumed the pulp to be an incompressible Newtonian fluid with a density of r=750 kg/m3 and a viscosity of m=0.04 kg/（m2·s）[8]. Finally， we chose the k-e two-equation as the turbulence model[9].
3.3 Mesh generation
In order to increase the computational accuracy， grooves and bars areas need more mesh than the other parts of the refining zone.
Fig.3 and Table 2 show the mesh generation results of the five different refining discs.
4 Results and discussion 4.1 Cut plots and velocity curves
In order to get a more detailed view of the flow inside the refining zone， we used a Y-Z plane to create flow velocity cut plots.
According to the cut plots of the refining zones （Fig.4） and using the Point Target function of Flow-simulation， the pulp velocity was extracted on the radial of the disc per 10 mm. The pulp velocity curves are shown in Fig.5 and the velocity distribution is shown in Table 3.
4.2 Surface shear stress distribution
The disc refiner was applied on the pulp fibers through certain pressure conditions while the surface shear stress distribution on the disc suggested the effect of the refining bars on pulp[10]. During the pulping process， the rotating disc endured considerably more load than the stator. It is shown in previous studies that the pulp velocity on the rotating disc is much higher than that on the stator， therefore， in the actual production， the abrasion on the rotor is considerably more serious than that on the stator. This also partly reflects the problem of the bad environment of the rotating refining disc.
The surface shear stress distribution on the rotating refining disc， obtained by the simulations， is shown in Fig.6. The maximum and the mean value of the sheering stress is shown in Table 4.
Over all， the refining discs without dam such as DISC-1， DISC-2， and DISC-4 affected the pulp fiber mainly at the edge of the bars while cutting effects were stronger than the defiber effects on the pulp fiber. The refining disc with dam， DISC-3， affected the pulp fiber mainly at the top surface of the bars while defiber effects were stronger than the cutting effects on the fiber. The pulp reflux is apparently， the average of the pulp velocity is lower than the refining disc with dam.
Radiation Lines Straight Bars and Isometric Parallel Straight Bars refining discs such as DISC-1 and DISC-2， had a higher pulping velocity and efficiency， but the flow line and the surface shear stress condition results showed some disadvantages. The pulp velocity is very high around the inlet of the refining zone and the edge of the bars had a concentration of stress which will have a negative effect on the short fiber pulps. Moreover， these types of refining discs have a low utilization rate of cutting length on the outer ring of the refining zone which will eventually lead to high resistance on the bars. Also， the shear stress was concentrated on the edge of the bars which will result in an over cut of the pulp fiber. As the radius increases， the bar rake angle of Arc bars refining discs， such as DISC-5， increases as well. Usually， at the outer ring of the Arc bars refining disc， the rake angle is more than 45°. When the rotor bars and the stator bars are counter changing during pulping， the angle of the intersection is over 90°. Imagine a pair of scissors which the two blades intersection angle is over 90°， it’s hard to cut a free state of fibers. Even in a setup with reversed arc grooves between the bars， there is only a beating effect on the cross between the bars and the reversed grooves section.
5 Conclusions
Based on a simplified model， five different factories， commonly using refining discs in low consistency pulping were simulated in the Computational Fluid Dynamics （CFD） software Flow-simulation. The pulp velocity and the surface sheer stress of the rotating discs were presented and compared with each other. The flow field in the refining zone of the disc refiner is combined with the perpendicular and parallel flow to the surface of the disc. The pulp velocity distribution in the refining zone showed that the pulp speed between the rotating disc grooves was faster than that in the gap； furthermore， the pulp speed in the gap is faster than that between the stator grooves. The flow tendency of the pulp between the bars and grooves is a spiral precession which is not obvious in the Arc bar refining disc. By analyzing advantages and disadvantages of different type of the refining discs， we provided a theoretical basis for selection of different refining discs in dealing with different type of pulp fiber from the side.
References
[1] LIANG Qian-hua. A New Type of Disc Refiner Plate and Its Manufacture Method[J]. China Pulp&Paper， 2012， 31（9）： 73-75.
[2] ZHONG Ying-jie， DU Jin-yan， ZHANG Xue-mei. CFD technology and application in modern industry[J]. Journal of Zhejiang University of Technology， 2003， 31（3）： 50-55.
[3] PAN De-wei， CHU Jia-peng， Chu Ran. A Exploration of Mechanism of Refining Based on Dynamic Pressure Theory[J].Transactions of China Pulp and Paper， 2011， 26（4）： 28-31.
[4] YAO Jun， WANG Ping. Methods of Measuring and Adjusting Plate Clearance of Disc Refiner[J]. China Pulp&Paper， 2012， 31（1）： 67-71.
[5] WANG Jia-hui， WANG Ping. Research on computer simulation disc refiner refining process[J]. Equipment Materiel， 2014， 33（6）： 16-19.
[6] Lewis P J， Danforth D W. Stock Preparation Analysis[J]. TAPPI， 2001， 45（3）： 185-188.
[7] Leider P J， Rihs J. Understanding the Disk Refiner. Part 1[J]. TAPPI， 2000， 43（9）： 98-102.
[8] Leider P J， Nissan A H. Understanding the Disk Refiner. Part 2[J]. TAPPI， 2000， 43（10）： 85-89.
[9] SHEN Li-xin. Bar design and choice of disc refiner plates[J]. Paper and Paper Making， 2001， 32（1）： 30-32.
[10] SU Zhao-you. Study on Computer Simulation of Disc Refiner and Design Theory and Method of Disc Refiner Plate[D]. Tianjin： Tianjin University of Science and Technology， 2013.
Keywords： pulping； disc refiner； bar structure； CFD
1 Introduction
Disc refiners have been widely used in the pulping and papermaking industry. The refining disc is a core component of a disc refiner. There have been extensive researches on refining discs including materials， manufacturing process， principles of the structure failure， arrangement of the bars and grooves， and energy consumption. The design and structure of a refining disc will directly affect the beating quality and energy efficiency of the disc refiner[1-4].
In recent years， Computational Fluid Dynamics （CFD） has become a decisive method for studying fluid motion and understanding flow regularity. Therefore， the CFD method has provided an efficient way of simulating and analyzing process fluid machinery. Research in CFD simulations on disc refiners of pulping process started late in China[5]. With the development of computer numerical simulation technology， the CFD method increasingly shows the advantages of studying the pulping process of the disc refiner.
Although the simulation of a macroscopic refining disc takes longer than that of a partial one， it can provide a realistic representation of the refining zone including the pulp velocity， stress condition， and the flow path. Using the 3D modeling software SOLIDWORKS and the CFD software Flow-simulation， five different macroscopic refining disc bar structures have been built and simulated under the same conditions.
2 Modeling
Differences between bar structure refining discs are roughly divided into five groups： Radiation Lines Straight Bars， Isometric Parallel Straight Bars， Isometric Parallel Straight Bars with Dam， “V” Type Bars， and Arc Bars. These five types of refining discs will be referred to from now on as DISC-1， DISC-2， DISC-3， DISC-4， DISC-5 shown in Fig.1. The five different bar structures of refining discs were built in SOLIDWORKS. Considering the complexity of the refining disc structure， particularity of the fluid， and the computational speed， the five refining discs were taper and bolt simplified. Furthermore， the discs were all simulated as flat bars to ensure the efficiency of the simulation progress. Table 1 shows the modeling parameters of the five refining discs.
3 Flow field settings
3.1 Basic settings
Initially we imported each pair of refining discs’ 3D model from SOLIDWORKS into Flow-simulation. We used Wizard to begin a setting procedure， selected the Internal flow in the Analysis type option， and selected Exclude Cavities Without Condition. In the Rotation option， we chose the geometric center of the disc as the rotation axis； finally we defined the surface roughness
（0 mm） and ignored the influence of the gravity.
3.2 Boundary conditions
Taking DISC-1 as an example （Fig.2） we set the boundary conditions in Flow-simulation are as follows.
（1） Inlet boundary conditions. The entrance is a circular cross section， flow rate is 0.01 m3/s.
（2） Outlet boundary conditions. We set the outer edge of refining zone as a free export （101325 Pa=1 atm）.
（3） Wall boundary conditions. We set the stator as a static， real wall （0 r/s in the coordinate system）. Furthermore， we set the rotor around the center axis of rotation （105 r/s）.
（4） Minimum gap. The minimum gap in the refining zone （gap between two discs） was set to 1 mm. Moreover， the results accuracy， 5-class， adaptive mesh technique of Flow-simulation， was set to automatically turn on.
It should be noted that there is no existing pulp fluid mathematical model in any CFD software as of yet. Researchers usually assumed the pulp as constant viscosity Newtonian fluid and analyzed it as such in CFD software. Results based on literatures[6-7] and simulations fit the experimental data properly. In this study we assumed the pulp to be an incompressible Newtonian fluid with a density of r=750 kg/m3 and a viscosity of m=0.04 kg/（m2·s）[8]. Finally， we chose the k-e two-equation as the turbulence model[9].
3.3 Mesh generation
In order to increase the computational accuracy， grooves and bars areas need more mesh than the other parts of the refining zone.
Fig.3 and Table 2 show the mesh generation results of the five different refining discs.
4 Results and discussion 4.1 Cut plots and velocity curves
In order to get a more detailed view of the flow inside the refining zone， we used a Y-Z plane to create flow velocity cut plots.
According to the cut plots of the refining zones （Fig.4） and using the Point Target function of Flow-simulation， the pulp velocity was extracted on the radial of the disc per 10 mm. The pulp velocity curves are shown in Fig.5 and the velocity distribution is shown in Table 3.
4.2 Surface shear stress distribution
The disc refiner was applied on the pulp fibers through certain pressure conditions while the surface shear stress distribution on the disc suggested the effect of the refining bars on pulp[10]. During the pulping process， the rotating disc endured considerably more load than the stator. It is shown in previous studies that the pulp velocity on the rotating disc is much higher than that on the stator， therefore， in the actual production， the abrasion on the rotor is considerably more serious than that on the stator. This also partly reflects the problem of the bad environment of the rotating refining disc.
The surface shear stress distribution on the rotating refining disc， obtained by the simulations， is shown in Fig.6. The maximum and the mean value of the sheering stress is shown in Table 4.
Over all， the refining discs without dam such as DISC-1， DISC-2， and DISC-4 affected the pulp fiber mainly at the edge of the bars while cutting effects were stronger than the defiber effects on the pulp fiber. The refining disc with dam， DISC-3， affected the pulp fiber mainly at the top surface of the bars while defiber effects were stronger than the cutting effects on the fiber. The pulp reflux is apparently， the average of the pulp velocity is lower than the refining disc with dam.
Radiation Lines Straight Bars and Isometric Parallel Straight Bars refining discs such as DISC-1 and DISC-2， had a higher pulping velocity and efficiency， but the flow line and the surface shear stress condition results showed some disadvantages. The pulp velocity is very high around the inlet of the refining zone and the edge of the bars had a concentration of stress which will have a negative effect on the short fiber pulps. Moreover， these types of refining discs have a low utilization rate of cutting length on the outer ring of the refining zone which will eventually lead to high resistance on the bars. Also， the shear stress was concentrated on the edge of the bars which will result in an over cut of the pulp fiber. As the radius increases， the bar rake angle of Arc bars refining discs， such as DISC-5， increases as well. Usually， at the outer ring of the Arc bars refining disc， the rake angle is more than 45°. When the rotor bars and the stator bars are counter changing during pulping， the angle of the intersection is over 90°. Imagine a pair of scissors which the two blades intersection angle is over 90°， it’s hard to cut a free state of fibers. Even in a setup with reversed arc grooves between the bars， there is only a beating effect on the cross between the bars and the reversed grooves section.
5 Conclusions
Based on a simplified model， five different factories， commonly using refining discs in low consistency pulping were simulated in the Computational Fluid Dynamics （CFD） software Flow-simulation. The pulp velocity and the surface sheer stress of the rotating discs were presented and compared with each other. The flow field in the refining zone of the disc refiner is combined with the perpendicular and parallel flow to the surface of the disc. The pulp velocity distribution in the refining zone showed that the pulp speed between the rotating disc grooves was faster than that in the gap； furthermore， the pulp speed in the gap is faster than that between the stator grooves. The flow tendency of the pulp between the bars and grooves is a spiral precession which is not obvious in the Arc bar refining disc. By analyzing advantages and disadvantages of different type of the refining discs， we provided a theoretical basis for selection of different refining discs in dealing with different type of pulp fiber from the side.
References
[1] LIANG Qian-hua. A New Type of Disc Refiner Plate and Its Manufacture Method[J]. China Pulp&Paper， 2012， 31（9）： 73-75.
[2] ZHONG Ying-jie， DU Jin-yan， ZHANG Xue-mei. CFD technology and application in modern industry[J]. Journal of Zhejiang University of Technology， 2003， 31（3）： 50-55.
[3] PAN De-wei， CHU Jia-peng， Chu Ran. A Exploration of Mechanism of Refining Based on Dynamic Pressure Theory[J].Transactions of China Pulp and Paper， 2011， 26（4）： 28-31.
[4] YAO Jun， WANG Ping. Methods of Measuring and Adjusting Plate Clearance of Disc Refiner[J]. China Pulp&Paper， 2012， 31（1）： 67-71.
[5] WANG Jia-hui， WANG Ping. Research on computer simulation disc refiner refining process[J]. Equipment Materiel， 2014， 33（6）： 16-19.
[6] Lewis P J， Danforth D W. Stock Preparation Analysis[J]. TAPPI， 2001， 45（3）： 185-188.
[7] Leider P J， Rihs J. Understanding the Disk Refiner. Part 1[J]. TAPPI， 2000， 43（9）： 98-102.
[8] Leider P J， Nissan A H. Understanding the Disk Refiner. Part 2[J]. TAPPI， 2000， 43（10）： 85-89.
[9] SHEN Li-xin. Bar design and choice of disc refiner plates[J]. Paper and Paper Making， 2001， 32（1）： 30-32.
[10] SU Zhao-you. Study on Computer Simulation of Disc Refiner and Design Theory and Method of Disc Refiner Plate[D]. Tianjin： Tianjin University of Science and Technology， 2013.