Numerical prediction of fiber motion in a branching channel flow of fiber suspensions

Fiber orientation and dispersion in the dilute fiber suspension that flows through a T-shaped branching channel are simulated numerically based on the slender-body theory. The simulated results are consistent qualitatively with the experimental data available in the literature. The results show that the spatial distribution of fibers is dependent on the fiber aspect ratio, but has no relation with the volume fraction of fiber. The content ratio of fibers near the upper wall increases monotonically with an increasing Re number, and the situation is reverse for the region near the bottom wall. The orientation of fibers depends on Re number, however, the function of fiber volume fraction and aspect ratio is negligible. The fibers near the wall and in the central region of the channel align along the flow direction at all times, but the fibers in the other parts of the channel tend to align along the flow direction only in the downstream region.

Numerical simulation and visualization of fiber suspension in a turbulent round jet

The turbulent properties of the fiber suspension in a turbulent round jet are numerically simulated and visualized, and some of the results are compared with the experimental data. The effects of the Reynolds number, fiber volume fraction, and aspect ratio are analyzed. The results show that the fiber injection in the flow has a delay effect on the streamwise velocity decay along the jet axis, and such an effect becomes more obvious with the increases in the fiber volume fraction and aspect ratio and the decrease in the Reynolds number. The flow with fibers shows an increase in the streamwise velocity along the radial direction, and the increase magnitude is directly proportional to the fiber volume fraction and aspect ratio and inversely proportional to the Reynolds number. The presence of fibers makes the turbulent kinetic energy and Reynolds stress increase, and the extent increases with the fiber volume fraction, Reynolds number, and fiber aspect ratio.

EFFECTS OF TENSOR CLOSURE MODELS AND 3-D ORIENTATION ON THE STABILITY OF FIBER SUSPENSIONS IN A CHANNEL FLOW

Three different kinds of closure model of fiber orientation tensors were applied to simulate numerically the hydrodynamic stability of fiber suspensions in a channel flow. The effects of closure models and three_dimensional (3_D) orientation distribution of fibers on the results of stability analysis were examined. It is found that the relationship of the behavior in hydrodynamic stability and the parameter of the fiber given by all the three models are the same. However, the attenuation of flow instability is most distinct using 3_D hybrid model because the orientation of the fiber departures from the flow direction, and least apparent using its 2_D counterpart for that the fibers show a tendency towards alignment with the flow direction in this case.

STABILITY ANALYSIS IN SPATIAL MODE FOR CHANNEL FLOW OF FIBER SUSPENSIONS

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.

NUMERICAL SIMULATION OF FLOW OF PULP FIBER SUSPENSIONS IN STOCK PUMP WITH SEMI-OPEN IMPELLER

The flow of pulp fiber suspensions with a consistency below 5% through a pump falls into the turbulent region. The 2-phase 3D turbulent flow of the mixture is simulated in the hydraulic components composed by suction chamber, front board, semi-impeller and volute casing for the first time. The pseudo-fluid model and the k-ε turbulent model are modified. Phase coupled SIMPLE algorithm is applied to make pressure-velocity correction equation. Based on the results of the numerical simulation, the distribution of velocity, pressure and density of liquid and particle phase are compared and analyzed. The flow analysis in the tip between front board and impeller is emphasized, which reflects the advantage of semi-open impeller when it transports 2-phase medium. This calculation result will be helpful for the design of pump impeller and the establishment of design method of centrifugal stock pump.

Orientation distribution of fibers and rheological property in fiber suspensions flowing in a turbulent boundary layer

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.

RESEARCH ON THE MOTION OF PARTICLES IN THE TURBULENT PIPE FLOW OF FIBER SUSPENSIONS

The motion of fibers in turbulent pipe flow was simulated by 3-D integral method based on the slender body theory and simplified model of turbulence.The orientation distribution of fibers in the computational area for different Re numbers was computed.The results which were consistent with the experimental ones show that the fluctuation velocity of turbulence cause fibers to orient randomly.The orientation distributions become broader as the Re number increases.Then the fluctuation velocity and angular velocity of fibers were obtained.Both are affected by the fluctuation velocity of turbulence.The fluctuation velocity intensity of fiber is stronger at longitudinal than at lateral,while it was opposite for the fluctuation angular velocity intensity of fibers.Finally,the spatial distribution of fiber was given.It is obvious that the fiber dispersion is strenghened with the increase of Re numbers.

Theoretical research on rotational dispersion coefficient of fiber in turbulent shear flow of fiber suspension

The rotational dispersion coefficient of the fiber in the turbulent shear flow of fiber suspension was studied theoretically. The function of correlation moment between the different fluctuating velocity gradients of the flow was built firstly. Then the expres- sion, dependent on the characteristic length, time, velocity and a dimensionless parameter related to the effect of wall, of rotational dispersion coefficient is derived. The derived expression of rotational dispersion coefficient can be employed to the inhomogeneous and non-isotropic turbulent flows. Furthermore it can be expanded to three-dimensional turbulent flows and serves the theoretical basis for solving the turbulent flow of fiber suspension.

RESEARCH ON DISTRIBUTION FUNCTION AND ORIENTATION TENSORS OF FIBER SUSPENSIONS IN WEDGE-SHAPED FLOW FIELD

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.

FIBER ORIENTATION DISTRIBUTIONS IN SLIT CHANNEL FLOWS WITH ABRUPT EXPANSION FOR FIBER SUSPENSIONS

The lattice Boltzmann method was used to investigate numerically the fiber orientation distributions in slit channel flows with abrupt expansion for fiber suspensions even in the concentrated regime. The channels have a thin slit geometry with 1：4 and 1：3 expansions. Both the interactions between fibers and that between fibers and channel walls were taken into consideration. Some of numerical results are qualitatively in agreement with the experiment data. It is found that most of fibers are aligned in the flow direction in all the suspensions in the entrance region of the expansion. Fiber orientation distributions, having different patterns in different regions of the flow, depend on the expansion ratio of the channel. The mechanical fiber-fiber interaction largely affects the fiber orientation in the downstream of the expansion and in the salient corner for the cases of concentrated suspensions. The hydrodynamic interaction plays an important role on the fiber orientation in the dilute suspension.

STABILITY IN THE CIRCULAR PIPE FLOW OF FIBER SUSPENSIONS

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.

NUMERICAL SIMULATION ON VELOCITIES OF TWO INTERACTING FIBERS IN FIBER SUSPENSION

A mathematical model was put forward to describe the mechanical interactionsof two contacting fibers, then a numerical simulation was carried out. The results of the simulationaccord with experimental results well. It turns out that the initial contacting point and theinitial orientation of the settling fiber have much effect on the translational and rotationalvelocities of the settling fiber, along with the increase in the length or the decrease in theradius of the fiber, the translational and rotational velocities of the settling fiber decrease; thesame trend remains when the viscosity of the solvent increases or the density of the fiberdecreases.

THE ORIENTATION DISTRIBUTION OF FIBER SUSPENSIONS AND ITSEFFECT ON THE CONSTITUTIVE RELATIONSHIP

The particle orientation distribution of fiber suspensions as well as the bulk stresses of fiber suspensions in the dilute planar converging channel flow in laminar regime, the semi-dilute planar shear flow in laminar regime and dilute planar shear flow in turbulent regime was investigated theoretically and numerically. The experiment on the viscosity of the semi-dilute suspensions of aspect ratio of 10 is performed.

ON INSTABILITY OF DILUTE FIBER SUSPENSIONS IN AN AXISYMMETRIC TAYLOR-COUETTE FLOW

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.

Orientation of the fiber suspending in the flow through a tube containing a sphere

Fiber suspensions flow through a tube containing a sphere in the dilute and concentrated regimes is simulated numerically with the Lattice Boltzmann Method （LBM）. The numerical results of fiber orientation distribution based on a statistical scheme are obtained and agree qualitatively with the experimental ones for the flow through a parallel plate channel comaining a cylinder. The results show that the sphere in the tube results in a change in the fiber orientation distribution downstream of the sphere along the flow and transverse directions. The influences of the sphere on the fiber orientation distribution are more significant for the concentrated suspensions than for the dilute one. The effect of the initial fiber orientations on the fiber orientation distribution is significant upstream of the sphere but small downstream of the sphere.