The distribution function and orientation tensor of fiber suspensions in wedge shaped flow field were computed . The results indicate that with time increasing, the fiber orient themselves to flow direction graduall...The distribution function and orientation tensor of fiber suspensions in wedge shaped flow field were computed . The results indicate that with time increasing, the fiber orient themselves to flow direction gradually. At the locations with same pole radii, the angle between fiber orientation and centerline, which occurs with the most probability, decreases with the pole angle increasing . At the locations with same pole angle, the angle between fiber orientation and centerline increases with the pole radii decreasing. The second order tensors get steady more quickly at the points where the velocity g radients are larger. At the locations with same pole angle, the steady values of orientation tensors are identical. At the locations with same pole radii is, streamline becomes flatter as the pole angle decreases.展开更多
A linear stability analysis on the circular pipe flow of fiber suspensions ispresented. The fiber orientation tensors are used to describe the characteristics of theorientation dislribution of fibers. The constitutive...A linear stability analysis on the circular pipe flow of fiber suspensions ispresented. The fiber orientation tensors are used to describe the characteristics of theorientation dislribution of fibers. The constitutive equation for the fiber suspensions is set upand the modified Orr-Sommerfeld stability equation is derived. An improved finite difference methodwith high order accuracy is employed to solve the e-quation. The Newtonian pipe Poiseuille flowcorresponding to H = 0 is also analyzed for comparison. The results reveal that the fiber additiveswill enhance the flow stability, the degree of enhancement becomes high with the increases of theparameter H which accounts for the fiber resistance to the stretching along its axis. Fibersuspensions with large H can suppress the influence of high Reynolds number on the flow stability.Particularly, fibers give a higher attenuation of the short waves of disturbance.展开更多
The structural features of fiber suspensions are dependent on the fiber alignment in the flows. In this work the orientation distribution function and orientation tensors for semi-concentrated fiber suspensions in ...The structural features of fiber suspensions are dependent on the fiber alignment in the flows. In this work the orientation distribution function and orientation tensors for semi-concentrated fiber suspensions in converging channel flow were calculated, and the evolutions of the fiber alignment and the bulk effective vis-cosity were analyzed. The results showed that the bulk stress and the effective viscosity were functions of therate-of-strain tensor and the fiber orientation state ; and that the fiber suspensions evolved to steady alignment and tended to concentrate to some preferred directions close to but not same as the directions of local stream-lines. The bulk effective viscosity depended on the product of Reynolds number and time. The decrease of ef-fective viscosity near the boundary benefited the increase of the rate of flow. Finally when the fiber alignment went into steady state, the structural features of fiber suspensions were not dependent on the Reynolds numberbut on the converging channel angle.展开更多
The equations for fiber suspensions in an evolving mixing layer were solved by the spectral method, and the trajectory and orientation of fibers were calculated based on the slender body theory. The calculated spatial...The equations for fiber suspensions in an evolving mixing layer were solved by the spectral method, and the trajectory and orientation of fibers were calculated based on the slender body theory. The calculated spatial and orientation distributions of fibers are consistent with the experimental ones that were performed in this paper. The relationship between the microstructure of fibers and additional stress was examined. The results show that the spatial and orientation distributions of fibers are heterogeneous because of the influence of coherent vortices in the flow, which leads to the heterogeneity of the additional stress. The degree of heterogeneity increases with the increasing of St number and fiber aspect ratio. The fibers in the flow make the momentum loss thickness of the mixing layer thicker and accelerate the vorticity dispersion.展开更多
Different from previous temporal evolution assumption, the spatially growing mode was employed to analyze the linear stability for the channel flow of fiber suspensions. The stability equation applicable to fiber susp...Different from previous temporal evolution assumption, the spatially growing mode was employed to analyze the linear stability for the channel flow of fiber suspensions. The stability equation applicable to fiber suspensions was established and solutions for a wide range of Reynolds number and angular frequency were given numerically . The results show that, the flow instability is governed by a parameter H which represents a ratio between the axial stretching resistance of fiber and the inertial force of the fluid. An increase of H leads to a raise of the critical Reynolds number, a decrease of corresponding wave number, a slowdown of the decreasing of phase velocity , a growth of the spatial attenuation rate and a diminishment of the peak value of disturbance velocity. Although the unstable region is reduced on the whole, long wave disturbances are susceptible to fibers.展开更多
A stability analysis of flow between two coaxial rotating cylinders in the presence of fibers was performed. Based on the axisymmetric normal mode for the disturbances, a modified stability equation was derived. Then ...A stability analysis of flow between two coaxial rotating cylinders in the presence of fibers was performed. Based on the axisymmetric normal mode for the disturbances, a modified stability equation was derived. Then the numerical solution of the eigenvalue problem about the equation was obrained using the fourth order finite difference scheme. The marginal curves that determine the instability property were drawn. The results show that the flow instability of the dilute fiber suspensions is governed by the aspect ratio of fiber H, the inerement of H causes an increase of critical inner Reynohts number. The fiber additives effectively attenuate the instability of the flow. which is in agreement with those of related experiments.展开更多
The available expressions for the effective vis-cosity can not provide good predictions compared with the experiment data measured in the semi-dilute shear flows of fiber suspension with small aspect ratio. The depart...The available expressions for the effective vis-cosity can not provide good predictions compared with the experiment data measured in the semi-dilute shear flows of fiber suspension with small aspect ratio. The departure of the theoretical prediction from the measured data increases with the decrease of the fiber aspect ratio. Therefore, by experi-ment for the fiber with 20 mm diameter, a new expression for the effective viscosity in the semi-dilute shear flows of fiber suspension with small aspect ratio is proposed, the relation-ship between the shear viscosity of fiber suspensions and the fiber concentration is given. The results show that the effec-tive viscosity is not a linear function of the fiber concentra-tion.展开更多
The linear stability of fiber suspensions between two concentric cylinders rotating independently is studied. The modified stability equation is obtained based on the fiber orientation model and Hinch-Leal closure app...The linear stability of fiber suspensions between two concentric cylinders rotating independently is studied. The modified stability equation is obtained based on the fiber orientation model and Hinch-Leal closure approximation. The primary instabilities and bicritical curves have been calculated numerically. The critical Reynolds number,wavenumber and wave speeds of fiber suspensions as functions of the aspect ratio,volume concentration of the fibers and the gap width of cylinders are obtained.展开更多
The linear stability analysis of the fiber suspension Taylor-Couette flow against axisymmetric and non-axisymmetric disturbances is investigated. A generalized complex eigenvalue problem generated from the linearized ...The linear stability analysis of the fiber suspension Taylor-Couette flow against axisymmetric and non-axisymmetric disturbances is investigated. A generalized complex eigenvalue problem generated from the linearized set of the three-dimensional governing system equations around the basic Couette azimuthal solution are solved numerically with the Chebyshev spectral method. In a wide range of radius ratios and the magnitudes of counter rotating, critical bifurcation thresholds from the axisymmetric Couette flow to the flow with different azimuthal wave numbers are obtained. The complex dispersion relations of the linearized stability equation system for vortex patterns with different azimuthal wave number are calculated for real axial wave numbers for axially extended vortex structures.展开更多
An analysis of the instability in the Taylor-Couette flow of fiber suspensions with respect to the non-axisymmetric disturbances was performed. The constitutive model proposed by Ericksen was used to represent the rol...An analysis of the instability in the Taylor-Couette flow of fiber suspensions with respect to the non-axisymmetric disturbances was performed. The constitutive model proposed by Ericksen was used to represent the role of fiber additives on the stress tensor. The generalized eigenvalue equation governing the hydrodynamic stability of the system was solved using a direct numerical procedure. The results showed that the fiber additives can suppress the instability of the flow. At the same time, the non-axisymmetric disturbance is the preferred mode that makes the fiber suspensions unstable when the ratio of the angular ve- locity of the outer cylinder to that of the inner cylinder is a large negative number.展开更多
A model relating the translational and rotational transport of orientation distribution function （ODF） of fibers to the gradient of mean ODF and the dispersion coefficients is proposed to derive the mean equation fo...A model relating the translational and rotational transport of orientation distribution function （ODF） of fibers to the gradient of mean ODF and the dispersion coefficients is proposed to derive the mean equation for the ODE Then the ODF of fibers is predicted by numerically solving the mean equation for the ODF together with the equations of turbulent boundary layer flow. Finally the shear stress and first normal stress difference of fiber suspensions are obtained. The results, some of which agree with the available relevant experimental data, show that the most fibers tend to orient to the flow direction. The fiber aspect ratio and Reynolds number have significant and negligible effects on the orientation dis- tribution of fibers, respectively. The additional normal stress due to the presence of fibers is anisotropic. The shear stress of fiber suspension is larger than that of Newtonian solvent, and the first normal stress difference is much less than the shear stress. Both the additional shear stress and the first normal stress difference increase with increasing the fiber concentration and decreasing fiber aspect ratio.展开更多
In this study,we improved the dispersibility of the stocks in the headbox of an inclined wire machine to produce a distinct paper,and analyzed some factors affecting paper formation in the production of multiply paper...In this study,we improved the dispersibility of the stocks in the headbox of an inclined wire machine to produce a distinct paper,and analyzed some factors affecting paper formation in the production of multiply paper.We used FLUENT6.3 to analyze the flow of the stocks in the headbox and select the structure of the diffusion part required for improving the dispersibility of fibers.Moreover,based on a simulation experiment,the optimal rational angle of the diffusion part(g)was found to be approximately 8°~10°,and it improved the paper formation in the case of usage of two plates.Using the equation for the formation of paper layers in the headbox of an inclined wire machine,we obtained a paper with the given basic weight by controlling the inclined angle of the wire(a),initial height of water(H),and concentration of the stocks.We considered the effect of a and H of the stocks in the headbox on the fiber distribution,and according to the results,a should be set as approximately 20°~30°and H should be maximally high.When producing multi-ply paper by a wire,the line pressure of the couch roll should be maintained at 1.8~2.0 kN/m to avoid the damage to the paper sheets.In addition,we found the optimal structure parameter of the dehydrated roll was as follows:hole ratio of approximately 30%of the dehydrated roll surface area,width of 1.5~2.0 mm,slot pitch of 5~6 mm,slot depth of 2~3 mm,and inclined angle of diffusion part(b)of 5°.展开更多
基金Project supported by the National Natural Science Foundation for Outstanding Youth of China. (Grant No: 19925210)
文摘The distribution function and orientation tensor of fiber suspensions in wedge shaped flow field were computed . The results indicate that with time increasing, the fiber orient themselves to flow direction gradually. At the locations with same pole radii, the angle between fiber orientation and centerline, which occurs with the most probability, decreases with the pole angle increasing . At the locations with same pole angle, the angle between fiber orientation and centerline increases with the pole radii decreasing. The second order tensors get steady more quickly at the points where the velocity g radients are larger. At the locations with same pole angle, the steady values of orientation tensors are identical. At the locations with same pole radii is, streamline becomes flatter as the pole angle decreases.
文摘A linear stability analysis on the circular pipe flow of fiber suspensions ispresented. The fiber orientation tensors are used to describe the characteristics of theorientation dislribution of fibers. The constitutive equation for the fiber suspensions is set upand the modified Orr-Sommerfeld stability equation is derived. An improved finite difference methodwith high order accuracy is employed to solve the e-quation. The Newtonian pipe Poiseuille flowcorresponding to H = 0 is also analyzed for comparison. The results reveal that the fiber additiveswill enhance the flow stability, the degree of enhancement becomes high with the increases of theparameter H which accounts for the fiber resistance to the stretching along its axis. Fibersuspensions with large H can suppress the influence of high Reynolds number on the flow stability.Particularly, fibers give a higher attenuation of the short waves of disturbance.
文摘The structural features of fiber suspensions are dependent on the fiber alignment in the flows. In this work the orientation distribution function and orientation tensors for semi-concentrated fiber suspensions in converging channel flow were calculated, and the evolutions of the fiber alignment and the bulk effective vis-cosity were analyzed. The results showed that the bulk stress and the effective viscosity were functions of therate-of-strain tensor and the fiber orientation state ; and that the fiber suspensions evolved to steady alignment and tended to concentrate to some preferred directions close to but not same as the directions of local stream-lines. The bulk effective viscosity depended on the product of Reynolds number and time. The decrease of ef-fective viscosity near the boundary benefited the increase of the rate of flow. Finally when the fiber alignment went into steady state, the structural features of fiber suspensions were not dependent on the Reynolds numberbut on the converging channel angle.
基金The project supported by the Doctoral Program of Higher Education in China(20030335001)
文摘The equations for fiber suspensions in an evolving mixing layer were solved by the spectral method, and the trajectory and orientation of fibers were calculated based on the slender body theory. The calculated spatial and orientation distributions of fibers are consistent with the experimental ones that were performed in this paper. The relationship between the microstructure of fibers and additional stress was examined. The results show that the spatial and orientation distributions of fibers are heterogeneous because of the influence of coherent vortices in the flow, which leads to the heterogeneity of the additional stress. The degree of heterogeneity increases with the increasing of St number and fiber aspect ratio. The fibers in the flow make the momentum loss thickness of the mixing layer thicker and accelerate the vorticity dispersion.
基金Foundation item: the National Natural Science Foundation of China for Outstanding Young Sci-entists (19925210)
文摘Different from previous temporal evolution assumption, the spatially growing mode was employed to analyze the linear stability for the channel flow of fiber suspensions. The stability equation applicable to fiber suspensions was established and solutions for a wide range of Reynolds number and angular frequency were given numerically . The results show that, the flow instability is governed by a parameter H which represents a ratio between the axial stretching resistance of fiber and the inertial force of the fluid. An increase of H leads to a raise of the critical Reynolds number, a decrease of corresponding wave number, a slowdown of the decreasing of phase velocity , a growth of the spatial attenuation rate and a diminishment of the peak value of disturbance velocity. Although the unstable region is reduced on the whole, long wave disturbances are susceptible to fibers.
基金Project supported by the National Natural Science Foundation of China (Grant No :19372090) .
文摘A stability analysis of flow between two coaxial rotating cylinders in the presence of fibers was performed. Based on the axisymmetric normal mode for the disturbances, a modified stability equation was derived. Then the numerical solution of the eigenvalue problem about the equation was obrained using the fourth order finite difference scheme. The marginal curves that determine the instability property were drawn. The results show that the flow instability of the dilute fiber suspensions is governed by the aspect ratio of fiber H, the inerement of H causes an increase of critical inner Reynohts number. The fiber additives effectively attenuate the instability of the flow. which is in agreement with those of related experiments.
文摘The available expressions for the effective vis-cosity can not provide good predictions compared with the experiment data measured in the semi-dilute shear flows of fiber suspension with small aspect ratio. The departure of the theoretical prediction from the measured data increases with the decrease of the fiber aspect ratio. Therefore, by experi-ment for the fiber with 20 mm diameter, a new expression for the effective viscosity in the semi-dilute shear flows of fiber suspension with small aspect ratio is proposed, the relation-ship between the shear viscosity of fiber suspensions and the fiber concentration is given. The results show that the effec-tive viscosity is not a linear function of the fiber concentra-tion.
基金Project (Nos. 10632070 and 40231017) supported by the National Natural Science Foundation of China
文摘The linear stability of fiber suspensions between two concentric cylinders rotating independently is studied. The modified stability equation is obtained based on the fiber orientation model and Hinch-Leal closure approximation. The primary instabilities and bicritical curves have been calculated numerically. The critical Reynolds number,wavenumber and wave speeds of fiber suspensions as functions of the aspect ratio,volume concentration of the fibers and the gap width of cylinders are obtained.
基金the Major Programof the National Natural Science Foundation of China with Grant No10632070
文摘The linear stability analysis of the fiber suspension Taylor-Couette flow against axisymmetric and non-axisymmetric disturbances is investigated. A generalized complex eigenvalue problem generated from the linearized set of the three-dimensional governing system equations around the basic Couette azimuthal solution are solved numerically with the Chebyshev spectral method. In a wide range of radius ratios and the magnitudes of counter rotating, critical bifurcation thresholds from the axisymmetric Couette flow to the flow with different azimuthal wave numbers are obtained. The complex dispersion relations of the linearized stability equation system for vortex patterns with different azimuthal wave number are calculated for real axial wave numbers for axially extended vortex structures.
基金Project (No. 10372090) supported by the National Natural ScienceFoundation of China
文摘An analysis of the instability in the Taylor-Couette flow of fiber suspensions with respect to the non-axisymmetric disturbances was performed. The constitutive model proposed by Ericksen was used to represent the role of fiber additives on the stress tensor. The generalized eigenvalue equation governing the hydrodynamic stability of the system was solved using a direct numerical procedure. The results showed that the fiber additives can suppress the instability of the flow. At the same time, the non-axisymmetric disturbance is the preferred mode that makes the fiber suspensions unstable when the ratio of the angular ve- locity of the outer cylinder to that of the inner cylinder is a large negative number.
基金The project supported by the Major Program of National Natural Science Foundation of China(10632070)
文摘A model relating the translational and rotational transport of orientation distribution function （ODF） of fibers to the gradient of mean ODF and the dispersion coefficients is proposed to derive the mean equation for the ODE Then the ODF of fibers is predicted by numerically solving the mean equation for the ODF together with the equations of turbulent boundary layer flow. Finally the shear stress and first normal stress difference of fiber suspensions are obtained. The results, some of which agree with the available relevant experimental data, show that the most fibers tend to orient to the flow direction. The fiber aspect ratio and Reynolds number have significant and negligible effects on the orientation dis- tribution of fibers, respectively. The additional normal stress due to the presence of fibers is anisotropic. The shear stress of fiber suspension is larger than that of Newtonian solvent, and the first normal stress difference is much less than the shear stress. Both the additional shear stress and the first normal stress difference increase with increasing the fiber concentration and decreasing fiber aspect ratio.
文摘In this study,we improved the dispersibility of the stocks in the headbox of an inclined wire machine to produce a distinct paper,and analyzed some factors affecting paper formation in the production of multiply paper.We used FLUENT6.3 to analyze the flow of the stocks in the headbox and select the structure of the diffusion part required for improving the dispersibility of fibers.Moreover,based on a simulation experiment,the optimal rational angle of the diffusion part(g)was found to be approximately 8°~10°,and it improved the paper formation in the case of usage of two plates.Using the equation for the formation of paper layers in the headbox of an inclined wire machine,we obtained a paper with the given basic weight by controlling the inclined angle of the wire(a),initial height of water(H),and concentration of the stocks.We considered the effect of a and H of the stocks in the headbox on the fiber distribution,and according to the results,a should be set as approximately 20°~30°and H should be maximally high.When producing multi-ply paper by a wire,the line pressure of the couch roll should be maintained at 1.8~2.0 kN/m to avoid the damage to the paper sheets.In addition,we found the optimal structure parameter of the dehydrated roll was as follows:hole ratio of approximately 30%of the dehydrated roll surface area,width of 1.5~2.0 mm,slot pitch of 5~6 mm,slot depth of 2~3 mm,and inclined angle of diffusion part(b)of 5°.
