- Email: [email protected]
Evaluation of effect of paddle element stagger angle on the local velocity profiles in a twin-screw continuous mixer with viscous flow using Finite Element Method simulations
Journal of Food Engineering 108 (2012) 585–599
Contents lists available at ScienceDirect
Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng
Evaluation of effect of paddle element stagger angle on the local velocity profiles in a twin-screw continuous mixer with viscous flow using Finite Element Method simulations Kiran V. Vyakaranam, Bharani K. Ashokan, Jozef L. Kokini ⇑ Department of Food Science, Rutgers University, 65 Dudley Rd., New Brunswick, NJ 08901, United States
a r t i c l e
i n f o
Article history: Received 7 August 2010 Received in revised form 3 November 2010 Accepted 1 December 2010 Available online 13 December 2010 Keywords: Velocity profiles Mixing Twin-screw Stagger Newtonian Viscous flow 3D FEM simulation Laser Doppler Anemometry
a b s t r a c t The effect of paddle element geometry, specifically a systematic change in stagger angle, on the velocity distribution of a Newtonian corn syrup was evaluated in the mixing region of a 200 Readco continuous processor using 3D FEM simulations. Local velocities and regions of backflow were compared for three configurations of the paddle elements in the mixing region consisting of nine pairs of paddle elements with the central three being in a neutral (FLAT), staggered 45° forward (45F) or staggered 45° reverse (45R) configuration. The total material flow rate through the mixer was independent of the paddle element stagger but increased with screw speed when the mixer was operated with the barrel fully filled. The stagger angle variation caused only local disturbances in axial flow. The overall magnitudes of velocity were highest for the FLAT configuration followed by 45F and 45R. The local X and Y velocity components in the region of stagger showed no significant variation with paddle element stagger while the Z velocity component varied significantly in this region. Increased forward flow was seen for the 45F configuration while significant local backflow was seen for the 45R configuration at all positions of the paddle element rotation. The FLAT configuration had greater levels of pressure in the intermeshing region, suggesting a squeeze flow while there were not significant variations in pressure for the 45F and 45R configurations, suggesting a predominantly conveying/leakage flow in the axial direction. Variation in local flows is critical to good mixing. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction A mixing process involves blending or distribution of ingredients, creation of structure and dispersion/size-reduction of ingredients. When highly structured materials such as dough and heavy pastes are involved, the mixing process of these often highly viscous materials is usually in the laminar region and requires mixing elements that are carefully designed to create the desired flow to optimize the efficiency of the mixer. Twin screw continuous mixers, although being similar in design to twin screw extruders, are primarily used to attain a good degree of mixing and homogeneity in viscous food materials whereas twin screw extruders are generally designed to melt, cook, plasticize and shape food materials. In the food industry the twin screw mixers, like the ReadcoÒ continuous processor, are used for chewing gum base manufacture (Song and Townsend, 1996), melt crystallization of sugar alcohols
⇑ Corresponding author. Present address: College of Agriculture, Consumer and Environmental Sciences, 228 Mumford Hall, 1301 W. Gregory Drive, Urbana, IL 61801, United States. Tel.: +1 217 333 0240; fax: +1 217 333 5816. E-mail address: [email protected] (J.L. Kokini). 0260-8774/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2010.12.001
like xylitol and mannitol (DuRoss, 1991, 1992), chocolate conching (Zeigler and Aguilar, 2003), etc. The efficiency of a mixing device can be evaluated through the flow profiles generated in the mixer volume. In particular the geometry and arrangement of kneading/mixing elements is of specific importance to flow in continuous mixer geometries because they cause local and overall variations in axial flow which can affect mixing efficiency. With recent advances in computational fluid dynamics, it is possible to evaluate the flow in complex mixing geometries like the twin screw continuous mixers using numerical simulation techniques, particularly the Finite Element Method (FEM). FEM has been widely used to study flow in batch mixers and dough kneaders with complex geometries. Connelly and Kokini (2006a) modeled the flow of a Newtonian, a power law and a cross-model fluid in the filled bowl of the Farinograph. A 41,860 element mesh was used for the Farinograph bowl while the two sigma blades were meshed with 6232 and 6166 mesh elements, respectively. The mesh superposition technique was used to calculate the velocity, shear rate and mixing data. FEM simulations were used to compare the flow and mixing in a 2D single screw mixer to a twin screw mixer, both modeled after the cross-section and paddle
586
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
shape of the Readco continuous processor. However since the simulations were 2D, axial flow was not considered (Connelly and Kokini, 2004). Much of the published literature dealing with FEM simulation of flow in continuous mixing geometries pertains to twin screw extruders used in polymer processing and the effect of screw design on the flow in the mixing region of twin-screw extruders. Gotsis et al. (1990) found that the use of 30° reverse staggered (left-handed) kneading blocks caused the ratio of local backflow to forward flow to be five times greater than that seen in a 30° forward staggered (right-handed) configuration. FEM simulations were used to solve the 3D flow of a Newtonian fluid. The study stopped at measuring velocity values and reported only velocity contours. The small backflow in the forward configuration was attributed to a block up action caused by the adjacent kneading block while this effect was greatly enhanced in the reverse stagger due to the formation of a reverse flow channel on the surface. Yao and Manas-Zloczower (1998) analyzed the effect of ‘pushing’ and ‘counter-pushing’ units on the flow profile (among other mixing parameters), in an LCMAX 40 axial discharge continuous twin-screw mixer using the FIDAP CFD analysis package. While no backflow was observed in the cross-sections analyzed,
Fig. 1. The ReadcoÒ 200 continuous processor (twin-screw mixer) shown here with a transparent Plexiglas barrel.
it was found that using three or more counter pushing units in a total configuration of six units affected the pumping capacity of the mixer. The absence of backflow could have been due to the fact that these elements consisted of a screw design that was a hybrid between fully-flighted screws and kneading block elements, unlike individually stacked kneading blocks where gaps between the staggered elements create channels for backflow. Bravo et al. (2004) compared the effect of the kneading element width on the flow in a five element kneading block region of a twin-screw extruder configured with a forward stagger angle of 45° between successive elements. An increase in the width of the disc elements generally increased the amount of backflow. While it was further hypothesized that an increase in the stagger angle between the kneading blocks would increase the backflow by creating larger gaps with local pressure gradients, no comparison was given between staggered and non-staggered arrangements. More recently, Zhang et al. (2009) used particle tracking in FEM flow simulations of kneading block region of a twin screw extruder to compute the residence time distribution and the distributive mixing efficiency. No information was presented on the velocity profiles. Not much published work is available on the analysis of flow in continuous mixers. Although similar in design to the twin-screw extruder, the Readco Continuous processor significantly different in terms of (i) larger dimensions and greater barrel and flow channel volume; (ii) negligible axial pressure gradient and absence of constrained die at discharge end. With developments such as mesh superposition and more powerful numerical techniques it is appropriate to revisit the prediction of flow profiles and mixing efficiencies amongst kneading elements as a function of stagger angle. The objective of this study was to investigate the local pressure and velocity profiles developed in the kneading/mixing elements in the mixing region of the Readco 200 continuous processor, which is a co-rotating continuous pilot size mixer built with larger screw and barrel dimensions and wider kneading/mixing elements exclusively aimed at viscous fluid mixing. The mixer’s typical screw configuration consists of full flight conveying screw elements and kneading blocks or mixing elements. The conveying screw elements are always positive displacement elements that are needed for the net positive flow of the material through the barrel. Specifically a three part mixing element configuration was studied where a 45° forward or reverse stagger angle was introduced in the central part while keeping the beginning and end of the mixing region not staggered. Velocity profiles for an isothermal Newtonian vis-
Fig. 2. Conveying screw elements and the 9 pairs of neutral paddle elements of the Readco twin-screw mixer shown here with the barrel removed.
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
cous flow were computed through 3D FEM simulations of the flow and the effect of paddle element stagger is visualized and compared in the entire mixer volume, specific local cross-sections and along the axial length of the mixer.
587
2. Materials and methods Three-dimensional numerical simulations of the time dependent, isothermal flow in the mixing region of the ReadcoÒ 200 pro-
Fig. 3. (a) 3D single paddle mesh with a total of 432 3 mesh elements, (b) 3D three paddle mesh with a total of 432 5 mesh elements, (c) radial mesh of the XY crosssection of the barrel volume with the convex intermeshing region and a total of 1072 elements, (d) barrel volume mesh, and (e) axial profile of the barrel volume mesh showing regions of axial mesh intervals of 3 and 5, gap between paddle elements and the entrance and exit extensions.
588
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
Table 1 LDA settings for measurement of velocity magnitudes in the continuous mixer.
Wavelength, k (nm) Number of fringes Fringe spacing (lm) Focal length of probe lens (mm) Frequency shift of Bragg cell (MHz)
Blue beam
Green beam
488 60 1.5602 120 40
514.5 60 1.6449
equipped with a 3.00 GHz IntelÒ Pentium D dual core processor. Newtonian corn syrup of viscosity 120 Pa s and density of 1420 kg/m3 was used as the model fluid in the simulation. Polyflow has been extensively used in several similar studies in our group that investigated viscous and viscoelastic flow during mixing and scale-up of extruders and batch and continuous mixers (Dhanasekharan and Kokini, 2000, 2003; Connelly and Kokini, 2003, 2004, 2006a,b, 2007) The FEM solver discretizes the flow domain using the finite elements technique and solves for conservation of mass and conservation of momentum:
rv ¼0 r r þ qf ¼ q
ð2:1Þ @v þ v rv @t
ð2:2Þ
where r is the stress tensor, q is the fluid density and f is the external body force tensor per unit mass. The stress tensor r can be defined in terms of the isotropic pressure (P) and the extra stress tensor (T) as
r ¼ PI þ T Fig. 4. Location of velocity measurement points using Laser Doppler Anemometry; All points on the mid-Z XY cross-sectional plane of the 4th flat paddle element A (3.74, 1.75), B (0.34, 1.75) and C (0.05, 1.59).
cessor (Fig. 1) were conducted using the Polyflow suite (AnsysFluent Inc., Lebanon, NH) which is a commercial CFD software specifically designed for simulating viscous mixing flows. The software suite includes the 3D mesh generator, Gambit, the Finite Element Method (FEM) solver, Polyflow and the post-processor, CFXPost. The simulations were run on a DELL workstation
ð2:3Þ
For a Newtonian fluid in an isothermal flow, the extra stress tensor (T) is given by
T ¼ 2lD
ð2:4Þ
where D is the rate of deformation tensor and l is the viscosity of the fluid. The mixing region of the ReadcoÒ 200 processor consisted of 9 pairs of 1/200 wide lens shaped or two-lobed, self-wiping paddles fitted onto co-rotating shafts and enclosed in a horizontal ‘8’ shaped barrel. The mixer barrel volume and the paddle elements were meshed individually and the mesh superposition technique (MST) was used in the flow simulation (Connelly and Kokini,
Fig. 5. Paddle element configurations in the mixing region of the ReadcoÒ 200 continuous processor. (a) FLAT – all paddle elements parallel to each other, (b) 45F – three center paddle elements in a forward stagger of 45°, and (c) 45R – three center paddle elements in a reverse stagger of 45°.
Fig. 6. Experimental mass flow rate of GlobeÒ Corn Syrup 042110 measured in the ReadcoÒ 200 continuous processor as a function of screw speed and paddle element configuration.
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
2004; Ashokan, 2008). The mesh superposition technique avoids the requirement of periodic re-meshing of the barrel volume during the movement of the paddles and will be described below. In the MST, first the velocities of all mesh points on the moving paddle elements are defined by the angular velocity (screw RPM) of the paddle elements. In the next step the velocities of those mesh points in the barrel volume that are swept by the moving elements is set equal to the velocity of the moving element mesh points. This is done by using a penalty term H in the equation of motion to modify Eq. (2.2) as follows:
Þ þ ð1 HÞðrP þ r T þ qg qaÞ ¼ 0 Hðv v
589
using a compression factor b, in order to satisfy mass conservation by making the fluid slightly compressible in regions of the flow domain where the velocity is modified to be equal to that of the moving paddle elements
ð2:5Þ
is the velocity of the moving paddles and the vaIn Eq. (2.4), v lue of H is set equal to 1 for all barrel volume mesh elements that are greater than 60% covered by the moving paddles, while it is set equal to 0 in all other cases. When H is equal to 1 then the simulation sees a solid block and when H is set to zero the simulation sees a deformable liquid. The continuity Eq. (2.1) is also modified
Fig. 8. Comparison of experimental and simulated velocities at point B (z = 3.9624 cm) (a) Vx and (b) Vz.
Fig. 7. Comparison of experimental and simulated velocities at point A (z = 3.9624 cm) (a) Vx, (b) Vy, and (c) Vz.
Fig. 9. Comparison of experimental and simulated velocities at point C (z = 3.9624 cm) (a) Vx and (b) Vz.
590
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
Table 2 %RMS of experimental and simulated velocity magnitudes Vx, Vy and Vz calculated at points A, B and C in the entire mixer as a function of axial position. RMS%
A
B
C
Z, cm
Vx
Vy
Vz
Vx
Vz
Vx
Vz
1.27 2.6162 3.9624 5.3086 6.6548
10.94 10.84 10.75 10.90 11.14
3.80 3.74 3.70 3.77 3.90
8.33 7.62 6.93 7.07 7.53
7.34 5.87 5.71 6.67 9.39
9.44 5.39 5.04 10.72 19.81
16.46 22.57 24.76 21.78 14.52
14.19 8.80 3.23 10.29 17.63
Velocity units (cm/s).
Table 3 Maximum and minimum values of total velocity magnitude (V) and Vx, Vy and Vz calculated at all points in the entire mixer volume for one complete revolution of the three paddle elements (FLAT, 45F and 45R). Paddle configuration
V
Vx
Vy
Vz
Max./ min.
Max./min.
Max./min.
Max./min.
FLAT
106.3/0
42.1/70.61
77.5/83.76
45F
71.89/0
45R
37.23/0
47.97/ 58.29 35.35/ 33.52
105/ 41.22.8 71.50/ 37.03 31.04/ 31.28
Velocity units (cm/s).
66.7/62.14 27.52/ 33.88
b
r V þ DP ¼ 0
l
ð2:6Þ
Here l is the local viscosity of the fluid. The recommended default value of the compression factor, b in Polyflow is 0.01. The value is chosen such that it is neither too low to cause false pressure peaks to appear in constrained regions nor too high to cause the fluid to be highly compressible. Fig. 2 shows the Conveying screw elements and the 9 pairs of neutral paddle elements of the ReadcoÒ twin-screw mixer with the barrel removed. The co-ordinate system is defined with the axial material flow direction as the direction of +Z, and the +Y axis coming out of the image plane. The shafts rotate in a clockwise direction when looking into the direction of flow, or +Z. The nine mixing elements will be named P1, P2,. . ., P9 with the numbers increasing in the +Z direction. Fig. 3a shows an individual paddle element mesh. The XY cross-section of the paddle was meshed with a total of 432 mesh elements and extended in the +Z direction with three mesh intervals. Due to a limitation in the Polyflow software that allows for only 10 moving parts, three pairs of the individually meshed paddle elements were fused together with an axial mesh interval of five and used for the non-staggered regions at the beginning (P1, P2, and P3) and at the end (P7, P8, and P9) of the mixing region (Fig. 3b). The center three paddle element pairs (P4, P5, and P6) were not fused in order allow for individual stagger. Fig. 3c shows the simulation mesh used for the 2D XY cross-section of the barrel volume, meshed with a total of 1072 mesh elements using 10 mesh intervals in the radial direction that included 2 intervals for the boundary layer, while 56 mesh intervals were used in the
Fig. 10. Velocity vector maps for the FLAT configuration at (a) time step 1, 10° rotation, (b) time step 4, 40° rotation, and (c) time step 9, 90° rotation.
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
591
Fig. 11. Velocity vector maps for the 45F configuration at (a) time step 1, 10° rotation, (b) time step 4, 40° rotation, and (c) time step 9, 90° rotation.
azimuthal direction. The intermeshing region was further finely meshed to avoid mesh elements being covered by the two paddles at the same time. This included a convex mesh with boundary lay-
ers on the inner side where both paddles could enter at the same time and four adjoining quadrants where only one paddle would be present at a given time. The incorporation of the boundary layer
Fig. 12. Velocity vector maps for the 45R configuration at (a) time step 1, 10° rotation, (b) time step 4, 40° rotation, and (c) time step 9, 90° rotation.
592
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
Fig. 13. Pressure contours over x = 0 and y = 0 cross-sectional planes in the FLAT configuration at (a) time step 1, 10° rotation, (b) time step 4, 40° rotation, (c) time step 9, 90° rotation, (d) time step 10, 100° rotation, (e) 45F configuration at time step 4, 40° rotation and (d) 45R configuration at time step 4, 40° rotation.
into the convex region ensured that there were always two mesh elements in the gap between the paddle elements. The meshed
XY cross-section was extended into 3D to cover entire barrel volume. The axial mesh interval of the barrel volume was set equal
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
to coincide with the individual (3) and the fused (5) paddle regions. The gap between individual paddle elements, which is 0.0762 cm as measured in the Readco mixer, was meshed with an interval of 2. In order to isolate the paddle elements from entrance and exit effects, the axial length of the barrel volume mesh was extended on both sides to include a 2 mesh interval equal to half the length of a single paddle element (0.635 cm). An experimental validation step was performed at three points in the mixer wherein velocities were experimentally measured and compared to the simulated velocity magnitudes and the %RMS difference was calculated. Velocity measurements in the ReadcoÒ 200 continuous processor were made using a 300 mW, two color Argon ion Laser Doppler Anemometor (Dantec Dynamics, Mahwah, NJ). In the LDA technique, two sets of laser beams are emitted by the probe with each set in a plane perpendicular to the other. The beams create light and dark inference fringes in the volume of fluid enclosed by the intersecting beams. The frequency of the light scattered by the fluid particles crossing this volume is measured by the probe and converted to velocity magnitudes. Since each set of beams was projected into the barrel perpendicular to the other, it was possible to determine two directional components of the velocity in a single measurement. The settings of the LDA system are shown in Table 1. The LDA probe was fitted onto a computer controlled traverse which could be moved in the x, y and z directions to a precision of 1 mm. An encoder was fitted to the mixer shafts which recorded the relative angular position of the paddle elements (or the degrees of rotation). The mixer was fitted with a Plexiglas barrel and was fully filled with the transparent corn syrup and operated at 100 rpm. LDA velocity measurements were ta-
593
ken at three points in the plane of the 4th paddle pair from the inlet – A (3.74, 1.75, mid-z of the paddle), B (0.34, 1.75, mid-z of the paddle) and C (0.05, 1.59, mid-z of the paddle) (Fig. 4). These points were identified as representative of various locations in the mixer (point A is in the clearance region between the barrel wall and paddle while points B and C are in the intermeshing region, with B closer to the barrel wall) and the velocity components at these locations were calculated. The %RMS difference between the experimental and simulated velocity magnitudes was calculated using the following equations
RMS ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi P 2 n ðv s v e Þ
RMS% ¼
n RMS 100 ðv emax v emin Þ
ð2:7Þ
ð2:8Þ
where vs and ve represent the local simulated and the experimental velocity magnitudes, respectively, and n is the number of points of measurement. The individually meshed paddle elements constituting a total of 10 moving parts fused together were superimposed onto the barrel volume mesh in an initial starting orientation (Fig. 5). The simulation was solved for one full revolution of the elements in 36 steps at every 10° movement of the paddles which constitutes a single ‘time step’. Gravitational forces were neglected and the density was set equal to the fluid density of corn syrup. Due to the absence of the conveying screw region in the simulation, experimentally measured liquid flow rate for the corn syrup was imposed on the
Fig. 14. Contour maps of Vx at P4 and time step 4, 40° rotation for (b) FLAT (c) 45F and (d) 45R configurations.
594
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
Fig. 15. Contour maps of Vy at P4 and time step 4, 40° rotation for (b) FLAT (c) 45F and (d) 45R configurations.
inlet boundary plane with a fully developed velocity profile. Mass flow rate was experimentally measured as a function of screw speed for each paddle configuration in the mixer. Corn syrup stored at 22 °C was allowed to fill the mixer barrel completely before starting the mixer. About 2 min of fully filled flow was allowed through the mixer in order for the flow to reach steady state. The barrel was kept fully-filled throughout the run thus keeping the inflow rate constant. The time taken to collect approximately 400– 500 g of the material was used to calculate the mass flow rate and was converted into the volumetric flow rate using the density of the corn syrup. The walls of the barrel in the simulation were defined as impervious and stationary, while the rotational velocity of the paddles was set at 100 rpm. The time for one complete revolution was 0.6 s, so that the length of each time step was 0.01667 s. In order to study the effect of paddle element stagger on the flow profiles, three different paddle element configurations were used as shown in Fig. 5. The first of the three configurations (FLAT) had no stagger and was fully aligned with all the nine paddle elements configured parallel to each other. In the second configuration (45F), the first and the last three pairs of the paddle elements were kept same as the FLAT configuration while the center three elements were staggered at a clockwise/forward angle of 45° relative to the parallel elements in the direction of flow. Finally a third configuration (45R) was created similar to the 45F configuration except that the center three paddle elements were staggered at a counterclockwise/reverse 45° angle. During each full rotation of the mixer shafts the relative orientation of the paddle elements at a 10° rotation (time step 1) is equivalent to the relative orientation at rotation of 100° (time step 10), owing to the symmetry of the mixer geometry. Hence for the purpose of this study comparing
the effect of paddle element configuration on the local flow profile, investigation of the flow in the first nine time steps was deemed sufficient and was consistent with the method used by Yao and Manas-Zloczower (1998). Specifically, velocity profiles for each paddle configuration are compared at time steps 1, 4 and 9 (rotation of 10°, 40° and 90°) in order to simplify the analysis while at the same time include velocity profile information after a significant rotation of the paddle elements.
3. Results and discussion 3.1. Experimental flow rate and validation Fig. 6 shows a comparison of experimentally measured material flow rates for the three paddle configurations as a function of the screw speed. The flow rate was clearly dependent on the screw speed but was independent of the paddle element configuration. This is due to the fact that the barrel volume was always maintained fully filled and then the flow is purely conveying and is not driven by a net pressure gradient as would be the case in a static mixer. Thus with a constant inlet flow rate and discharge die opening, the overall flow rate through the mixer is strongly controlled by the conveying screws at and is not significantly affected by the stagger angle in the paddle elements. The measured average value of the volumetric flow rate at 100 RPM was used as the imposed inlet boundary condition in the numerical simulation to understand the local distribution of velocities. Figs. 7–9 show a comparison of the experimental and simulated velocity magnitudes at the three points A, B and C, respectively, at
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
595
Fig. 16. Contour maps of axial velocity (Vz) at P4 in the FLAT configuration (a) time step 1, 10° rotation, (b) time step 4, 40° rotation, and (c) time step 9, 90° rotation.
an axial position of z = 3.96 cm and for every 10° rotation of the paddle element rotation, ranging from 10° to 360°. As can be seen the simulated velocities and experimental velocities followed the same general trends with the magnitudes being similar in most cases, differing only slightly. Table 2 shows the RMS% difference between the simulated and experimental velocities. Higher differences in magnitudes between the experimental and simulation velocities were seen in vx magnitudes at particular paddle element positions when the beams were obstructed. Since the measurements were taken over several days, a slight error could have been introduced during the experimental setup, even though great care was taken to center the laser beams during each setup. It was not possible to measure the Vy data at points B and C due to their positioning in the intermeshing region, which meant the laser beams were always obstructed in the direction needed to measure the Vy. The maximum difference found in the experimental and simulated velocities at point A was around 10% and 4% in the X and Y directions, respectively, while in the axial Z velocities had an RMS% difference of a maximum of 5.5%. 3.2. Effect of paddle element stagger on the velocity profiles For each of the time steps (1, 4, and 9) we present here comparison of velocity profiles using velocity vector maps throughout the mixer volume, axial velocity contour maps at various XY cross-sec-
tions along the mixer axis, and axial velocity magnitudes along a line running through the nip region of the paddle elements along the length of the mixer. 3.2.1. Comparison of velocity magnitudes throughout the whole mixer Table 3 shows the comparison of the range of velocity magnitudes found in the entire mixer volume over one complete revolution of the screw. The FLAT configuration showed highest total velocity magnitudes followed by the 45F and the 45R configurations. The range of magnitudes of X, Y and Z components of velocity were also higher for the FLAT configuration compared to the staggered configurations, with the reverse 45R configuration showing the smallest ranges. This is thought to be due to the unobstructed channel flow in the FLAT configuration allowing for local regions with the highest velocity magnitudes. A visualization of the velocity vector maps is presented in Figs. 10–12 for the three screw configurations, each at time steps 1, 4 and 9. The vectors are color coded from dark blue to dark red corresponding to the global range of overall velocity magnitudes with a range from 0 to 120 cm/s combining the three paddle element configurations. The distribution of the velocity vectors shows that the flow generally follows the paddle surface with additional axial flow occurring in the intermeshing region between the paddles. In the FLAT configuration with no stagger, at the first time step a significant forward flow is seen in the first half of the mixing region
596
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
(P1–P4) caused by the imposed inflow boundary condition while in the latter half (P5–P9), a significant backward flow is observed. This is probably due to the material flowing back from the gap between the last paddle pair (P9) and the outflow plane. Fig. 13 shows the pressure profile over the x = 0 and y = 0 planes at time steps 1, 4, 9 and 10 for the FLAT configuration and at time step 4 for the 45F and 45R configurations. While the overall pressure levels are lower than typical extrusion processes (mainly due to the greater barrel volume and absence of constricted die as discussed earlier), the FLAT configuration shows increased pressure zones in the intermeshing region. This suggests that the flow mechanism involves the material being squeezed into and out of the intermeshing region causing increased axial flow. Fig. 13 also shows the pressure profiles at time step 10 (100° rotation) which is symmetric to the profile at time step 1 (10° rotation) showing that the flow profile is cyclic with a period of 90°. In the forward 45° stagger configuration (45F), significant regions of increased forward flow are seen in the ‘intermeshing region’ between the paddle elements at all the three time steps, especially in the middle of the mixing region right after P4 where the stagger angle is introduced. In contrast, regions of backflow can be seen in the reverse 45° stagger configuration (45R) at the beginning and towards the end of the staggered region (P4 and P7). The pressure profiles over the x = 0 and y = 0 cross-sectional planes for 45F and 45R configurations from Fig. 13 show that there is little variation in the pressure for both the configurations. While the pressure profiles shown here are only for time step 4, the trend
was similar at all time steps. This suggests that the local axial forward and backflow in the staggered regions seems to be caused by gaps that appear in the intermeshing region between two consecutive staggered paddles. 3.2.2. Comparison of local velocity magnitudes over XY planar crosssections XY planar cross-sections of the mixing region were analyzed for the distribution of local X, Y and Z velocities (Vx, Vy, and Vz). Figs. 14 and 15 show the contour maps of magnitudes of the X and Y velocity components (Vx and Vy) at the 4th paddle element (P4) after a rotation of 40° (time step 4) The cross-section can be divided into three broad regions of flow activity – the ‘C’ shaped region between the paddle element and the barrel wall, the ‘intermeshing region’ between the co-rotating paddle elements and the ‘nip’ regions which is the narrow, constricted gap between the paddle tips and the barrel surface. While the distribution of both Vx and Vy was as expected in relation to the rotating paddle elements, there was also no significant variation of the range of local velocity magnitudes among the three configurations. The highest magnitudes of positive and negative Vx were just above the average values in all the three configurations while magnitudes of Vy significantly greater than the average values were seen around the leading and trailing edges of the paddle elements. Figs. 16–18 show contour maps of the local axial velocity flow (Vz) on the XY cross-sectional plane at the 4th paddle pair location at times steps 1, 4 and 9. In the FLAT configuration, only a slight
Fig. 17. Contour maps of axial velocity (Vz) at P4 in the 45F configuration (a) time step 1, 10° rotation, (b) time step 4, 40° rotation, and (c) time step 9, 90° rotation.
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
increase in the axial velocities is seen in the ‘C’ shaped region between the paddle elements and the barrel wall and no significant regions of increased forward or backward flow are seen in the intermeshing regions between the paddle elements over all the times steps. This confirms that most of the axial flow in the FLAT configurations happens through the ‘C’ shaped region between the paddle elements and the barrel wall in comparison to the intermeshing region. In the 45F configuration, at the P4 region, which is the beginning of the staggered region, high values of forward axial flow are concentrated in the intermeshing region between the paddle elements at all the three time steps. A similar distribution of backward flow is seen in the intermeshing region for the reverse 45R configuration at all the time steps. This result again points to the increased local forward flow and backflow channels created in the intermeshing region due to the stagger in the paddles. The amount of local backflow in the reverse stagger configuration is somewhat lesser than the amount of increased local forward flow regions found in the same regions for the forward stagger configuration due to the net axial flow imposed in the +Z direction that acts on reducing the backflow intensity. As a direct result of this, there is significantly greater axial flow in the C-shaped region between the paddle element and the barrel wall compared to the forward 45F. The local axial velocities in the intermeshing region throughout the barrel volume were computed along a line running through the nip region in the Z direction for the three time steps (Fig. 19).
597
Fig. 19 shows the evolution of Vz along this line from time step 1 through 9 for the three configurations. In all the three configurations, the axial velocity went from positive at time step 1 to neutral at time step 4 to negative values at time step 4 at the beginning of the mixing region (z = 0–4 cm; inlet boundary plane to P3). A converse common trend towards the end of the mixing region (z = 9– 13.8 cm; P8 to outlet boundary plane) where the axial velocity magnitudes increased from negative to positive. This shows the pumping action of the non-staggered region involving periodic cycles of forward and backward flow. Significant influence of the stagger can be seen in middle of the mixing region (z = 4–9 cm; P4–P7). While the FLAT configuration showed continuous transition of the axial velocity along the axial length, the forward 45F showed increased local forward flow and the reverse 45R configuration showed increased backward flow at all the time steps. 4. Conclusions 3D FEM simulations were used to study the effect of stagger angle on the flow profile in a Readco 200 continuous processor. The analysis of velocity profiles shows that an introduction of stagger (forward or reverse) in a limited region of the mixing region can only create local disruptions in overall flow and not enough to create an overall forward or reverse flow. This is especially owing to the fact that a constant flow is imposed at the inlet boundary plane of the mixing region in the simulation. In the actual mixer, this in-
Fig. 18. Contour maps of axial velocity (Vz) at P4 in the 45R configuration (a) time step 1, 10° rotation, (b) time step 4, 40° rotation, and (c) time step 9, 90° rotation.
598
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
Fig. 19. Axial velocity (Vz) along a line running through the nip region of the mixer (a) FLAT (b) 45F and (c) 45R configuration at 10°, 40° and 90° rotation of the paddle elements.
let flow into the mixing region is caused by the conveying screw elements that precede the 9 paddle element pair mixing region. As expected, a measurement of the material flow rate also proved to be independent of the introduction of the stagger in the paddle elements and varied only with the screw speed. Paddle element stagger primarily caused variations in the local axial velocity (Vz) values while local Vx and Vy remained largely unaffected. The local variations in velocities also depend on the specific time step (or paddle rotation) implying that flow information must be analyzed at all dissimilar angular positions of the paddle elements after accounting for geometrical symmetry. The material flow in the FLAT configuration is mostly unobstructed and hence shows a greater axial velocity increase along the axis whereas the stagger causes obstruction to the axial flow in specific regions, depending on the type and location of the stagger. Local pressure profiles showed greater pressure values in the intermeshing region of the FLAT configuration, suggesting the material is squeezed into and out of the region. The overall axial
transport in the FLAT configuration happened through the Cshaped region between the paddle elements and the barrel wall while in the forward 45F configuration, the axial transport of the material was mostly through the intermeshing region between the co-rotating paddle elements. In case of the reverse 45R configuration, significant local backflow regions were seen in the intermeshing region which also resulted in the axial flow happening through the C-shaped region between the paddle elements and the barrel wall. There was no significant variation of for pressure in the axial direction for both the staggered configurations suggesting a conveying/leakage mechanism for axial transport. The specific location of the local variations in axial flow is of significance to further analysis of local and overall dispersive and distributive mixing indices. The location and length of the staggered region could affect the distribution and intensity of increased local forward and backward flow. In our simulation, the staggered region constituted only 1/3 of the entire mixing region and additionally was in the middle of two equal length non-staggered regions.
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
It would be interesting to see the effect of the length of the staggered region and also the location in relation to presence of nonstaggered regions. Acknowledgements This research was supported by the National Research Initiative of the USDA Cooperative State Research, Education and Extension Service, Grant #2003-35503-13907 References Ashokan, B.K., 2008. Developing Methods for Design and Analysis of Continuous Mixers through 3D Numerical Simulation of Flow and Mixing. PhD Thesis, Rutgers University. Bravo, V.L., Hrymak, A.N., Wright, J.D., 2004. Study of particle trajectories, residence times and flow behavior in kneading discs of intermeshing co-rotating twinscrew extruders. Polymer Engineering and Science 44 (4), 779–793. Connelly, R.K., Kokini, J.L., 2003. 2-D numerical simulation of differential viscoelastic fluids in a single-screw continuous mixer: application of viscoelastic finite element methods. Advances in Polymer Technology 22 (1), 22–41. Connelly, R.K., Kokini, J.L., 2004. The effect of shear thinning and differential viscoelasticity on mixing in a model 2D mixer as determined using FEM with particle tracking. Journal of Non-Newtonian Fluid Mechanics 123 (1), 1–17. Connelly, R.K., Kokini, J.L., 2006a. Mixing simulation of a viscous Newtonian liquid in a twin sigma blade mixer. AIChE Journal 52 (10), 3383–3393.
599
Connelly, R.K., Kokini, J.L., 2006b. 3D numerical simulation of the flow of viscous Newtonian and shear thinning fluids in a twin sigma blade mixer. Advances in Polymer Technology 25 (3), 182–194. Connelly, R.K., Kokini, J.L., 2007. Examination of the mixing ability of single and twin screw mixers using 2D finite element method simulation with particle tracking. Journal of Food Engineering 79 (3), 956–969. Dhanasekharan, M., Kokini, J.L., 2000. Viscoelastic flow modeling in the extrusion of a dough-like fluid. Journal of Food Process Engineering 23 (3), 237– 247. Dhanasekharan, M., Kokini, J.L., 2003. Design and scaling of wheat dough extrusion by numerical simulation of flow and heat transfer. Journal of Food Engineering 60 (4), 421–430. DuRoss, J.W., 1991. Mannitol having Gamma Sorbitol Polymorph. United States Patent 5023,092 DuRoss, J.W., 1992. Melt Crystallized Xylitol. United States Patent 5139,795 Gotsis, A.D., Ji, Z., Kalyon, M., 1990. 3-D analysis of the flow in co-rotating twinscrew extruders. Society of Plastics Engineers ANTEC Technical Papers 36, 139– 142. Song, J.H., Townsend, D.J., 1996. Continuous Gum Base Manufacture Using Paddle Mixing. United States Patent 5571543. Yao, C.-H., Manas-Zloczower, I., 1998. Influence of design on dispersive mixing performance in an axial discharge continuous mixer – LCMAX 40. Polymer Engineering and Science 38 (6), 936–946. Zeigler, G.R., Aguilar, C.A., 2003. Residence time distribution in a co-rotating twin screw continuous mixer by the step change method. Journal of Food Engineering 59, 161–167. Zhang, X., Feng, L., Chen, W., Hu, G., 2009. Numerical simulation and experimental validation of mxing performance of kneading discs in a twin screw extruder. Polymer Engineering and Science 49 (9), 1772–1783.
Contents lists available at ScienceDirect
Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng
Evaluation of effect of paddle element stagger angle on the local velocity profiles in a twin-screw continuous mixer with viscous flow using Finite Element Method simulations Kiran V. Vyakaranam, Bharani K. Ashokan, Jozef L. Kokini ⇑ Department of Food Science, Rutgers University, 65 Dudley Rd., New Brunswick, NJ 08901, United States
a r t i c l e
i n f o
Article history: Received 7 August 2010 Received in revised form 3 November 2010 Accepted 1 December 2010 Available online 13 December 2010 Keywords: Velocity profiles Mixing Twin-screw Stagger Newtonian Viscous flow 3D FEM simulation Laser Doppler Anemometry
a b s t r a c t The effect of paddle element geometry, specifically a systematic change in stagger angle, on the velocity distribution of a Newtonian corn syrup was evaluated in the mixing region of a 200 Readco continuous processor using 3D FEM simulations. Local velocities and regions of backflow were compared for three configurations of the paddle elements in the mixing region consisting of nine pairs of paddle elements with the central three being in a neutral (FLAT), staggered 45° forward (45F) or staggered 45° reverse (45R) configuration. The total material flow rate through the mixer was independent of the paddle element stagger but increased with screw speed when the mixer was operated with the barrel fully filled. The stagger angle variation caused only local disturbances in axial flow. The overall magnitudes of velocity were highest for the FLAT configuration followed by 45F and 45R. The local X and Y velocity components in the region of stagger showed no significant variation with paddle element stagger while the Z velocity component varied significantly in this region. Increased forward flow was seen for the 45F configuration while significant local backflow was seen for the 45R configuration at all positions of the paddle element rotation. The FLAT configuration had greater levels of pressure in the intermeshing region, suggesting a squeeze flow while there were not significant variations in pressure for the 45F and 45R configurations, suggesting a predominantly conveying/leakage flow in the axial direction. Variation in local flows is critical to good mixing. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction A mixing process involves blending or distribution of ingredients, creation of structure and dispersion/size-reduction of ingredients. When highly structured materials such as dough and heavy pastes are involved, the mixing process of these often highly viscous materials is usually in the laminar region and requires mixing elements that are carefully designed to create the desired flow to optimize the efficiency of the mixer. Twin screw continuous mixers, although being similar in design to twin screw extruders, are primarily used to attain a good degree of mixing and homogeneity in viscous food materials whereas twin screw extruders are generally designed to melt, cook, plasticize and shape food materials. In the food industry the twin screw mixers, like the ReadcoÒ continuous processor, are used for chewing gum base manufacture (Song and Townsend, 1996), melt crystallization of sugar alcohols
⇑ Corresponding author. Present address: College of Agriculture, Consumer and Environmental Sciences, 228 Mumford Hall, 1301 W. Gregory Drive, Urbana, IL 61801, United States. Tel.: +1 217 333 0240; fax: +1 217 333 5816. E-mail address: [email protected] (J.L. Kokini). 0260-8774/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2010.12.001
like xylitol and mannitol (DuRoss, 1991, 1992), chocolate conching (Zeigler and Aguilar, 2003), etc. The efficiency of a mixing device can be evaluated through the flow profiles generated in the mixer volume. In particular the geometry and arrangement of kneading/mixing elements is of specific importance to flow in continuous mixer geometries because they cause local and overall variations in axial flow which can affect mixing efficiency. With recent advances in computational fluid dynamics, it is possible to evaluate the flow in complex mixing geometries like the twin screw continuous mixers using numerical simulation techniques, particularly the Finite Element Method (FEM). FEM has been widely used to study flow in batch mixers and dough kneaders with complex geometries. Connelly and Kokini (2006a) modeled the flow of a Newtonian, a power law and a cross-model fluid in the filled bowl of the Farinograph. A 41,860 element mesh was used for the Farinograph bowl while the two sigma blades were meshed with 6232 and 6166 mesh elements, respectively. The mesh superposition technique was used to calculate the velocity, shear rate and mixing data. FEM simulations were used to compare the flow and mixing in a 2D single screw mixer to a twin screw mixer, both modeled after the cross-section and paddle
586
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
shape of the Readco continuous processor. However since the simulations were 2D, axial flow was not considered (Connelly and Kokini, 2004). Much of the published literature dealing with FEM simulation of flow in continuous mixing geometries pertains to twin screw extruders used in polymer processing and the effect of screw design on the flow in the mixing region of twin-screw extruders. Gotsis et al. (1990) found that the use of 30° reverse staggered (left-handed) kneading blocks caused the ratio of local backflow to forward flow to be five times greater than that seen in a 30° forward staggered (right-handed) configuration. FEM simulations were used to solve the 3D flow of a Newtonian fluid. The study stopped at measuring velocity values and reported only velocity contours. The small backflow in the forward configuration was attributed to a block up action caused by the adjacent kneading block while this effect was greatly enhanced in the reverse stagger due to the formation of a reverse flow channel on the surface. Yao and Manas-Zloczower (1998) analyzed the effect of ‘pushing’ and ‘counter-pushing’ units on the flow profile (among other mixing parameters), in an LCMAX 40 axial discharge continuous twin-screw mixer using the FIDAP CFD analysis package. While no backflow was observed in the cross-sections analyzed,
Fig. 1. The ReadcoÒ 200 continuous processor (twin-screw mixer) shown here with a transparent Plexiglas barrel.
it was found that using three or more counter pushing units in a total configuration of six units affected the pumping capacity of the mixer. The absence of backflow could have been due to the fact that these elements consisted of a screw design that was a hybrid between fully-flighted screws and kneading block elements, unlike individually stacked kneading blocks where gaps between the staggered elements create channels for backflow. Bravo et al. (2004) compared the effect of the kneading element width on the flow in a five element kneading block region of a twin-screw extruder configured with a forward stagger angle of 45° between successive elements. An increase in the width of the disc elements generally increased the amount of backflow. While it was further hypothesized that an increase in the stagger angle between the kneading blocks would increase the backflow by creating larger gaps with local pressure gradients, no comparison was given between staggered and non-staggered arrangements. More recently, Zhang et al. (2009) used particle tracking in FEM flow simulations of kneading block region of a twin screw extruder to compute the residence time distribution and the distributive mixing efficiency. No information was presented on the velocity profiles. Not much published work is available on the analysis of flow in continuous mixers. Although similar in design to the twin-screw extruder, the Readco Continuous processor significantly different in terms of (i) larger dimensions and greater barrel and flow channel volume; (ii) negligible axial pressure gradient and absence of constrained die at discharge end. With developments such as mesh superposition and more powerful numerical techniques it is appropriate to revisit the prediction of flow profiles and mixing efficiencies amongst kneading elements as a function of stagger angle. The objective of this study was to investigate the local pressure and velocity profiles developed in the kneading/mixing elements in the mixing region of the Readco 200 continuous processor, which is a co-rotating continuous pilot size mixer built with larger screw and barrel dimensions and wider kneading/mixing elements exclusively aimed at viscous fluid mixing. The mixer’s typical screw configuration consists of full flight conveying screw elements and kneading blocks or mixing elements. The conveying screw elements are always positive displacement elements that are needed for the net positive flow of the material through the barrel. Specifically a three part mixing element configuration was studied where a 45° forward or reverse stagger angle was introduced in the central part while keeping the beginning and end of the mixing region not staggered. Velocity profiles for an isothermal Newtonian vis-
Fig. 2. Conveying screw elements and the 9 pairs of neutral paddle elements of the Readco twin-screw mixer shown here with the barrel removed.
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
cous flow were computed through 3D FEM simulations of the flow and the effect of paddle element stagger is visualized and compared in the entire mixer volume, specific local cross-sections and along the axial length of the mixer.
587
2. Materials and methods Three-dimensional numerical simulations of the time dependent, isothermal flow in the mixing region of the ReadcoÒ 200 pro-
Fig. 3. (a) 3D single paddle mesh with a total of 432 3 mesh elements, (b) 3D three paddle mesh with a total of 432 5 mesh elements, (c) radial mesh of the XY crosssection of the barrel volume with the convex intermeshing region and a total of 1072 elements, (d) barrel volume mesh, and (e) axial profile of the barrel volume mesh showing regions of axial mesh intervals of 3 and 5, gap between paddle elements and the entrance and exit extensions.
588
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
Table 1 LDA settings for measurement of velocity magnitudes in the continuous mixer.
Wavelength, k (nm) Number of fringes Fringe spacing (lm) Focal length of probe lens (mm) Frequency shift of Bragg cell (MHz)
Blue beam
Green beam
488 60 1.5602 120 40
514.5 60 1.6449
equipped with a 3.00 GHz IntelÒ Pentium D dual core processor. Newtonian corn syrup of viscosity 120 Pa s and density of 1420 kg/m3 was used as the model fluid in the simulation. Polyflow has been extensively used in several similar studies in our group that investigated viscous and viscoelastic flow during mixing and scale-up of extruders and batch and continuous mixers (Dhanasekharan and Kokini, 2000, 2003; Connelly and Kokini, 2003, 2004, 2006a,b, 2007) The FEM solver discretizes the flow domain using the finite elements technique and solves for conservation of mass and conservation of momentum:
rv ¼0 r r þ qf ¼ q
ð2:1Þ @v þ v rv @t
ð2:2Þ
where r is the stress tensor, q is the fluid density and f is the external body force tensor per unit mass. The stress tensor r can be defined in terms of the isotropic pressure (P) and the extra stress tensor (T) as
r ¼ PI þ T Fig. 4. Location of velocity measurement points using Laser Doppler Anemometry; All points on the mid-Z XY cross-sectional plane of the 4th flat paddle element A (3.74, 1.75), B (0.34, 1.75) and C (0.05, 1.59).
cessor (Fig. 1) were conducted using the Polyflow suite (AnsysFluent Inc., Lebanon, NH) which is a commercial CFD software specifically designed for simulating viscous mixing flows. The software suite includes the 3D mesh generator, Gambit, the Finite Element Method (FEM) solver, Polyflow and the post-processor, CFXPost. The simulations were run on a DELL workstation
ð2:3Þ
For a Newtonian fluid in an isothermal flow, the extra stress tensor (T) is given by
T ¼ 2lD
ð2:4Þ
where D is the rate of deformation tensor and l is the viscosity of the fluid. The mixing region of the ReadcoÒ 200 processor consisted of 9 pairs of 1/200 wide lens shaped or two-lobed, self-wiping paddles fitted onto co-rotating shafts and enclosed in a horizontal ‘8’ shaped barrel. The mixer barrel volume and the paddle elements were meshed individually and the mesh superposition technique (MST) was used in the flow simulation (Connelly and Kokini,
Fig. 5. Paddle element configurations in the mixing region of the ReadcoÒ 200 continuous processor. (a) FLAT – all paddle elements parallel to each other, (b) 45F – three center paddle elements in a forward stagger of 45°, and (c) 45R – three center paddle elements in a reverse stagger of 45°.
Fig. 6. Experimental mass flow rate of GlobeÒ Corn Syrup 042110 measured in the ReadcoÒ 200 continuous processor as a function of screw speed and paddle element configuration.
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
2004; Ashokan, 2008). The mesh superposition technique avoids the requirement of periodic re-meshing of the barrel volume during the movement of the paddles and will be described below. In the MST, first the velocities of all mesh points on the moving paddle elements are defined by the angular velocity (screw RPM) of the paddle elements. In the next step the velocities of those mesh points in the barrel volume that are swept by the moving elements is set equal to the velocity of the moving element mesh points. This is done by using a penalty term H in the equation of motion to modify Eq. (2.2) as follows:
Þ þ ð1 HÞðrP þ r T þ qg qaÞ ¼ 0 Hðv v
589
using a compression factor b, in order to satisfy mass conservation by making the fluid slightly compressible in regions of the flow domain where the velocity is modified to be equal to that of the moving paddle elements
ð2:5Þ
is the velocity of the moving paddles and the vaIn Eq. (2.4), v lue of H is set equal to 1 for all barrel volume mesh elements that are greater than 60% covered by the moving paddles, while it is set equal to 0 in all other cases. When H is equal to 1 then the simulation sees a solid block and when H is set to zero the simulation sees a deformable liquid. The continuity Eq. (2.1) is also modified
Fig. 8. Comparison of experimental and simulated velocities at point B (z = 3.9624 cm) (a) Vx and (b) Vz.
Fig. 7. Comparison of experimental and simulated velocities at point A (z = 3.9624 cm) (a) Vx, (b) Vy, and (c) Vz.
Fig. 9. Comparison of experimental and simulated velocities at point C (z = 3.9624 cm) (a) Vx and (b) Vz.
590
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
Table 2 %RMS of experimental and simulated velocity magnitudes Vx, Vy and Vz calculated at points A, B and C in the entire mixer as a function of axial position. RMS%
A
B
C
Z, cm
Vx
Vy
Vz
Vx
Vz
Vx
Vz
1.27 2.6162 3.9624 5.3086 6.6548
10.94 10.84 10.75 10.90 11.14
3.80 3.74 3.70 3.77 3.90
8.33 7.62 6.93 7.07 7.53
7.34 5.87 5.71 6.67 9.39
9.44 5.39 5.04 10.72 19.81
16.46 22.57 24.76 21.78 14.52
14.19 8.80 3.23 10.29 17.63
Velocity units (cm/s).
Table 3 Maximum and minimum values of total velocity magnitude (V) and Vx, Vy and Vz calculated at all points in the entire mixer volume for one complete revolution of the three paddle elements (FLAT, 45F and 45R). Paddle configuration
V
Vx
Vy
Vz
Max./ min.
Max./min.
Max./min.
Max./min.
FLAT
106.3/0
42.1/70.61
77.5/83.76
45F
71.89/0
45R
37.23/0
47.97/ 58.29 35.35/ 33.52
105/ 41.22.8 71.50/ 37.03 31.04/ 31.28
Velocity units (cm/s).
66.7/62.14 27.52/ 33.88
b
r V þ DP ¼ 0
l
ð2:6Þ
Here l is the local viscosity of the fluid. The recommended default value of the compression factor, b in Polyflow is 0.01. The value is chosen such that it is neither too low to cause false pressure peaks to appear in constrained regions nor too high to cause the fluid to be highly compressible. Fig. 2 shows the Conveying screw elements and the 9 pairs of neutral paddle elements of the ReadcoÒ twin-screw mixer with the barrel removed. The co-ordinate system is defined with the axial material flow direction as the direction of +Z, and the +Y axis coming out of the image plane. The shafts rotate in a clockwise direction when looking into the direction of flow, or +Z. The nine mixing elements will be named P1, P2,. . ., P9 with the numbers increasing in the +Z direction. Fig. 3a shows an individual paddle element mesh. The XY cross-section of the paddle was meshed with a total of 432 mesh elements and extended in the +Z direction with three mesh intervals. Due to a limitation in the Polyflow software that allows for only 10 moving parts, three pairs of the individually meshed paddle elements were fused together with an axial mesh interval of five and used for the non-staggered regions at the beginning (P1, P2, and P3) and at the end (P7, P8, and P9) of the mixing region (Fig. 3b). The center three paddle element pairs (P4, P5, and P6) were not fused in order allow for individual stagger. Fig. 3c shows the simulation mesh used for the 2D XY cross-section of the barrel volume, meshed with a total of 1072 mesh elements using 10 mesh intervals in the radial direction that included 2 intervals for the boundary layer, while 56 mesh intervals were used in the
Fig. 10. Velocity vector maps for the FLAT configuration at (a) time step 1, 10° rotation, (b) time step 4, 40° rotation, and (c) time step 9, 90° rotation.
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
591
Fig. 11. Velocity vector maps for the 45F configuration at (a) time step 1, 10° rotation, (b) time step 4, 40° rotation, and (c) time step 9, 90° rotation.
azimuthal direction. The intermeshing region was further finely meshed to avoid mesh elements being covered by the two paddles at the same time. This included a convex mesh with boundary lay-
ers on the inner side where both paddles could enter at the same time and four adjoining quadrants where only one paddle would be present at a given time. The incorporation of the boundary layer
Fig. 12. Velocity vector maps for the 45R configuration at (a) time step 1, 10° rotation, (b) time step 4, 40° rotation, and (c) time step 9, 90° rotation.
592
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
Fig. 13. Pressure contours over x = 0 and y = 0 cross-sectional planes in the FLAT configuration at (a) time step 1, 10° rotation, (b) time step 4, 40° rotation, (c) time step 9, 90° rotation, (d) time step 10, 100° rotation, (e) 45F configuration at time step 4, 40° rotation and (d) 45R configuration at time step 4, 40° rotation.
into the convex region ensured that there were always two mesh elements in the gap between the paddle elements. The meshed
XY cross-section was extended into 3D to cover entire barrel volume. The axial mesh interval of the barrel volume was set equal
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
to coincide with the individual (3) and the fused (5) paddle regions. The gap between individual paddle elements, which is 0.0762 cm as measured in the Readco mixer, was meshed with an interval of 2. In order to isolate the paddle elements from entrance and exit effects, the axial length of the barrel volume mesh was extended on both sides to include a 2 mesh interval equal to half the length of a single paddle element (0.635 cm). An experimental validation step was performed at three points in the mixer wherein velocities were experimentally measured and compared to the simulated velocity magnitudes and the %RMS difference was calculated. Velocity measurements in the ReadcoÒ 200 continuous processor were made using a 300 mW, two color Argon ion Laser Doppler Anemometor (Dantec Dynamics, Mahwah, NJ). In the LDA technique, two sets of laser beams are emitted by the probe with each set in a plane perpendicular to the other. The beams create light and dark inference fringes in the volume of fluid enclosed by the intersecting beams. The frequency of the light scattered by the fluid particles crossing this volume is measured by the probe and converted to velocity magnitudes. Since each set of beams was projected into the barrel perpendicular to the other, it was possible to determine two directional components of the velocity in a single measurement. The settings of the LDA system are shown in Table 1. The LDA probe was fitted onto a computer controlled traverse which could be moved in the x, y and z directions to a precision of 1 mm. An encoder was fitted to the mixer shafts which recorded the relative angular position of the paddle elements (or the degrees of rotation). The mixer was fitted with a Plexiglas barrel and was fully filled with the transparent corn syrup and operated at 100 rpm. LDA velocity measurements were ta-
593
ken at three points in the plane of the 4th paddle pair from the inlet – A (3.74, 1.75, mid-z of the paddle), B (0.34, 1.75, mid-z of the paddle) and C (0.05, 1.59, mid-z of the paddle) (Fig. 4). These points were identified as representative of various locations in the mixer (point A is in the clearance region between the barrel wall and paddle while points B and C are in the intermeshing region, with B closer to the barrel wall) and the velocity components at these locations were calculated. The %RMS difference between the experimental and simulated velocity magnitudes was calculated using the following equations
RMS ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi P 2 n ðv s v e Þ
RMS% ¼
n RMS 100 ðv emax v emin Þ
ð2:7Þ
ð2:8Þ
where vs and ve represent the local simulated and the experimental velocity magnitudes, respectively, and n is the number of points of measurement. The individually meshed paddle elements constituting a total of 10 moving parts fused together were superimposed onto the barrel volume mesh in an initial starting orientation (Fig. 5). The simulation was solved for one full revolution of the elements in 36 steps at every 10° movement of the paddles which constitutes a single ‘time step’. Gravitational forces were neglected and the density was set equal to the fluid density of corn syrup. Due to the absence of the conveying screw region in the simulation, experimentally measured liquid flow rate for the corn syrup was imposed on the
Fig. 14. Contour maps of Vx at P4 and time step 4, 40° rotation for (b) FLAT (c) 45F and (d) 45R configurations.
594
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
Fig. 15. Contour maps of Vy at P4 and time step 4, 40° rotation for (b) FLAT (c) 45F and (d) 45R configurations.
inlet boundary plane with a fully developed velocity profile. Mass flow rate was experimentally measured as a function of screw speed for each paddle configuration in the mixer. Corn syrup stored at 22 °C was allowed to fill the mixer barrel completely before starting the mixer. About 2 min of fully filled flow was allowed through the mixer in order for the flow to reach steady state. The barrel was kept fully-filled throughout the run thus keeping the inflow rate constant. The time taken to collect approximately 400– 500 g of the material was used to calculate the mass flow rate and was converted into the volumetric flow rate using the density of the corn syrup. The walls of the barrel in the simulation were defined as impervious and stationary, while the rotational velocity of the paddles was set at 100 rpm. The time for one complete revolution was 0.6 s, so that the length of each time step was 0.01667 s. In order to study the effect of paddle element stagger on the flow profiles, three different paddle element configurations were used as shown in Fig. 5. The first of the three configurations (FLAT) had no stagger and was fully aligned with all the nine paddle elements configured parallel to each other. In the second configuration (45F), the first and the last three pairs of the paddle elements were kept same as the FLAT configuration while the center three elements were staggered at a clockwise/forward angle of 45° relative to the parallel elements in the direction of flow. Finally a third configuration (45R) was created similar to the 45F configuration except that the center three paddle elements were staggered at a counterclockwise/reverse 45° angle. During each full rotation of the mixer shafts the relative orientation of the paddle elements at a 10° rotation (time step 1) is equivalent to the relative orientation at rotation of 100° (time step 10), owing to the symmetry of the mixer geometry. Hence for the purpose of this study comparing
the effect of paddle element configuration on the local flow profile, investigation of the flow in the first nine time steps was deemed sufficient and was consistent with the method used by Yao and Manas-Zloczower (1998). Specifically, velocity profiles for each paddle configuration are compared at time steps 1, 4 and 9 (rotation of 10°, 40° and 90°) in order to simplify the analysis while at the same time include velocity profile information after a significant rotation of the paddle elements.
3. Results and discussion 3.1. Experimental flow rate and validation Fig. 6 shows a comparison of experimentally measured material flow rates for the three paddle configurations as a function of the screw speed. The flow rate was clearly dependent on the screw speed but was independent of the paddle element configuration. This is due to the fact that the barrel volume was always maintained fully filled and then the flow is purely conveying and is not driven by a net pressure gradient as would be the case in a static mixer. Thus with a constant inlet flow rate and discharge die opening, the overall flow rate through the mixer is strongly controlled by the conveying screws at and is not significantly affected by the stagger angle in the paddle elements. The measured average value of the volumetric flow rate at 100 RPM was used as the imposed inlet boundary condition in the numerical simulation to understand the local distribution of velocities. Figs. 7–9 show a comparison of the experimental and simulated velocity magnitudes at the three points A, B and C, respectively, at
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
595
Fig. 16. Contour maps of axial velocity (Vz) at P4 in the FLAT configuration (a) time step 1, 10° rotation, (b) time step 4, 40° rotation, and (c) time step 9, 90° rotation.
an axial position of z = 3.96 cm and for every 10° rotation of the paddle element rotation, ranging from 10° to 360°. As can be seen the simulated velocities and experimental velocities followed the same general trends with the magnitudes being similar in most cases, differing only slightly. Table 2 shows the RMS% difference between the simulated and experimental velocities. Higher differences in magnitudes between the experimental and simulation velocities were seen in vx magnitudes at particular paddle element positions when the beams were obstructed. Since the measurements were taken over several days, a slight error could have been introduced during the experimental setup, even though great care was taken to center the laser beams during each setup. It was not possible to measure the Vy data at points B and C due to their positioning in the intermeshing region, which meant the laser beams were always obstructed in the direction needed to measure the Vy. The maximum difference found in the experimental and simulated velocities at point A was around 10% and 4% in the X and Y directions, respectively, while in the axial Z velocities had an RMS% difference of a maximum of 5.5%. 3.2. Effect of paddle element stagger on the velocity profiles For each of the time steps (1, 4, and 9) we present here comparison of velocity profiles using velocity vector maps throughout the mixer volume, axial velocity contour maps at various XY cross-sec-
tions along the mixer axis, and axial velocity magnitudes along a line running through the nip region of the paddle elements along the length of the mixer. 3.2.1. Comparison of velocity magnitudes throughout the whole mixer Table 3 shows the comparison of the range of velocity magnitudes found in the entire mixer volume over one complete revolution of the screw. The FLAT configuration showed highest total velocity magnitudes followed by the 45F and the 45R configurations. The range of magnitudes of X, Y and Z components of velocity were also higher for the FLAT configuration compared to the staggered configurations, with the reverse 45R configuration showing the smallest ranges. This is thought to be due to the unobstructed channel flow in the FLAT configuration allowing for local regions with the highest velocity magnitudes. A visualization of the velocity vector maps is presented in Figs. 10–12 for the three screw configurations, each at time steps 1, 4 and 9. The vectors are color coded from dark blue to dark red corresponding to the global range of overall velocity magnitudes with a range from 0 to 120 cm/s combining the three paddle element configurations. The distribution of the velocity vectors shows that the flow generally follows the paddle surface with additional axial flow occurring in the intermeshing region between the paddles. In the FLAT configuration with no stagger, at the first time step a significant forward flow is seen in the first half of the mixing region
596
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
(P1–P4) caused by the imposed inflow boundary condition while in the latter half (P5–P9), a significant backward flow is observed. This is probably due to the material flowing back from the gap between the last paddle pair (P9) and the outflow plane. Fig. 13 shows the pressure profile over the x = 0 and y = 0 planes at time steps 1, 4, 9 and 10 for the FLAT configuration and at time step 4 for the 45F and 45R configurations. While the overall pressure levels are lower than typical extrusion processes (mainly due to the greater barrel volume and absence of constricted die as discussed earlier), the FLAT configuration shows increased pressure zones in the intermeshing region. This suggests that the flow mechanism involves the material being squeezed into and out of the intermeshing region causing increased axial flow. Fig. 13 also shows the pressure profiles at time step 10 (100° rotation) which is symmetric to the profile at time step 1 (10° rotation) showing that the flow profile is cyclic with a period of 90°. In the forward 45° stagger configuration (45F), significant regions of increased forward flow are seen in the ‘intermeshing region’ between the paddle elements at all the three time steps, especially in the middle of the mixing region right after P4 where the stagger angle is introduced. In contrast, regions of backflow can be seen in the reverse 45° stagger configuration (45R) at the beginning and towards the end of the staggered region (P4 and P7). The pressure profiles over the x = 0 and y = 0 cross-sectional planes for 45F and 45R configurations from Fig. 13 show that there is little variation in the pressure for both the configurations. While the pressure profiles shown here are only for time step 4, the trend
was similar at all time steps. This suggests that the local axial forward and backflow in the staggered regions seems to be caused by gaps that appear in the intermeshing region between two consecutive staggered paddles. 3.2.2. Comparison of local velocity magnitudes over XY planar crosssections XY planar cross-sections of the mixing region were analyzed for the distribution of local X, Y and Z velocities (Vx, Vy, and Vz). Figs. 14 and 15 show the contour maps of magnitudes of the X and Y velocity components (Vx and Vy) at the 4th paddle element (P4) after a rotation of 40° (time step 4) The cross-section can be divided into three broad regions of flow activity – the ‘C’ shaped region between the paddle element and the barrel wall, the ‘intermeshing region’ between the co-rotating paddle elements and the ‘nip’ regions which is the narrow, constricted gap between the paddle tips and the barrel surface. While the distribution of both Vx and Vy was as expected in relation to the rotating paddle elements, there was also no significant variation of the range of local velocity magnitudes among the three configurations. The highest magnitudes of positive and negative Vx were just above the average values in all the three configurations while magnitudes of Vy significantly greater than the average values were seen around the leading and trailing edges of the paddle elements. Figs. 16–18 show contour maps of the local axial velocity flow (Vz) on the XY cross-sectional plane at the 4th paddle pair location at times steps 1, 4 and 9. In the FLAT configuration, only a slight
Fig. 17. Contour maps of axial velocity (Vz) at P4 in the 45F configuration (a) time step 1, 10° rotation, (b) time step 4, 40° rotation, and (c) time step 9, 90° rotation.
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
increase in the axial velocities is seen in the ‘C’ shaped region between the paddle elements and the barrel wall and no significant regions of increased forward or backward flow are seen in the intermeshing regions between the paddle elements over all the times steps. This confirms that most of the axial flow in the FLAT configurations happens through the ‘C’ shaped region between the paddle elements and the barrel wall in comparison to the intermeshing region. In the 45F configuration, at the P4 region, which is the beginning of the staggered region, high values of forward axial flow are concentrated in the intermeshing region between the paddle elements at all the three time steps. A similar distribution of backward flow is seen in the intermeshing region for the reverse 45R configuration at all the time steps. This result again points to the increased local forward flow and backflow channels created in the intermeshing region due to the stagger in the paddles. The amount of local backflow in the reverse stagger configuration is somewhat lesser than the amount of increased local forward flow regions found in the same regions for the forward stagger configuration due to the net axial flow imposed in the +Z direction that acts on reducing the backflow intensity. As a direct result of this, there is significantly greater axial flow in the C-shaped region between the paddle element and the barrel wall compared to the forward 45F. The local axial velocities in the intermeshing region throughout the barrel volume were computed along a line running through the nip region in the Z direction for the three time steps (Fig. 19).
597
Fig. 19 shows the evolution of Vz along this line from time step 1 through 9 for the three configurations. In all the three configurations, the axial velocity went from positive at time step 1 to neutral at time step 4 to negative values at time step 4 at the beginning of the mixing region (z = 0–4 cm; inlet boundary plane to P3). A converse common trend towards the end of the mixing region (z = 9– 13.8 cm; P8 to outlet boundary plane) where the axial velocity magnitudes increased from negative to positive. This shows the pumping action of the non-staggered region involving periodic cycles of forward and backward flow. Significant influence of the stagger can be seen in middle of the mixing region (z = 4–9 cm; P4–P7). While the FLAT configuration showed continuous transition of the axial velocity along the axial length, the forward 45F showed increased local forward flow and the reverse 45R configuration showed increased backward flow at all the time steps. 4. Conclusions 3D FEM simulations were used to study the effect of stagger angle on the flow profile in a Readco 200 continuous processor. The analysis of velocity profiles shows that an introduction of stagger (forward or reverse) in a limited region of the mixing region can only create local disruptions in overall flow and not enough to create an overall forward or reverse flow. This is especially owing to the fact that a constant flow is imposed at the inlet boundary plane of the mixing region in the simulation. In the actual mixer, this in-
Fig. 18. Contour maps of axial velocity (Vz) at P4 in the 45R configuration (a) time step 1, 10° rotation, (b) time step 4, 40° rotation, and (c) time step 9, 90° rotation.
598
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
Fig. 19. Axial velocity (Vz) along a line running through the nip region of the mixer (a) FLAT (b) 45F and (c) 45R configuration at 10°, 40° and 90° rotation of the paddle elements.
let flow into the mixing region is caused by the conveying screw elements that precede the 9 paddle element pair mixing region. As expected, a measurement of the material flow rate also proved to be independent of the introduction of the stagger in the paddle elements and varied only with the screw speed. Paddle element stagger primarily caused variations in the local axial velocity (Vz) values while local Vx and Vy remained largely unaffected. The local variations in velocities also depend on the specific time step (or paddle rotation) implying that flow information must be analyzed at all dissimilar angular positions of the paddle elements after accounting for geometrical symmetry. The material flow in the FLAT configuration is mostly unobstructed and hence shows a greater axial velocity increase along the axis whereas the stagger causes obstruction to the axial flow in specific regions, depending on the type and location of the stagger. Local pressure profiles showed greater pressure values in the intermeshing region of the FLAT configuration, suggesting the material is squeezed into and out of the region. The overall axial
transport in the FLAT configuration happened through the Cshaped region between the paddle elements and the barrel wall while in the forward 45F configuration, the axial transport of the material was mostly through the intermeshing region between the co-rotating paddle elements. In case of the reverse 45R configuration, significant local backflow regions were seen in the intermeshing region which also resulted in the axial flow happening through the C-shaped region between the paddle elements and the barrel wall. There was no significant variation of for pressure in the axial direction for both the staggered configurations suggesting a conveying/leakage mechanism for axial transport. The specific location of the local variations in axial flow is of significance to further analysis of local and overall dispersive and distributive mixing indices. The location and length of the staggered region could affect the distribution and intensity of increased local forward and backward flow. In our simulation, the staggered region constituted only 1/3 of the entire mixing region and additionally was in the middle of two equal length non-staggered regions.
K.V. Vyakaranam et al. / Journal of Food Engineering 108 (2012) 585–599
It would be interesting to see the effect of the length of the staggered region and also the location in relation to presence of nonstaggered regions. Acknowledgements This research was supported by the National Research Initiative of the USDA Cooperative State Research, Education and Extension Service, Grant #2003-35503-13907 References Ashokan, B.K., 2008. Developing Methods for Design and Analysis of Continuous Mixers through 3D Numerical Simulation of Flow and Mixing. PhD Thesis, Rutgers University. Bravo, V.L., Hrymak, A.N., Wright, J.D., 2004. Study of particle trajectories, residence times and flow behavior in kneading discs of intermeshing co-rotating twinscrew extruders. Polymer Engineering and Science 44 (4), 779–793. Connelly, R.K., Kokini, J.L., 2003. 2-D numerical simulation of differential viscoelastic fluids in a single-screw continuous mixer: application of viscoelastic finite element methods. Advances in Polymer Technology 22 (1), 22–41. Connelly, R.K., Kokini, J.L., 2004. The effect of shear thinning and differential viscoelasticity on mixing in a model 2D mixer as determined using FEM with particle tracking. Journal of Non-Newtonian Fluid Mechanics 123 (1), 1–17. Connelly, R.K., Kokini, J.L., 2006a. Mixing simulation of a viscous Newtonian liquid in a twin sigma blade mixer. AIChE Journal 52 (10), 3383–3393.
599
Connelly, R.K., Kokini, J.L., 2006b. 3D numerical simulation of the flow of viscous Newtonian and shear thinning fluids in a twin sigma blade mixer. Advances in Polymer Technology 25 (3), 182–194. Connelly, R.K., Kokini, J.L., 2007. Examination of the mixing ability of single and twin screw mixers using 2D finite element method simulation with particle tracking. Journal of Food Engineering 79 (3), 956–969. Dhanasekharan, M., Kokini, J.L., 2000. Viscoelastic flow modeling in the extrusion of a dough-like fluid. Journal of Food Process Engineering 23 (3), 237– 247. Dhanasekharan, M., Kokini, J.L., 2003. Design and scaling of wheat dough extrusion by numerical simulation of flow and heat transfer. Journal of Food Engineering 60 (4), 421–430. DuRoss, J.W., 1991. Mannitol having Gamma Sorbitol Polymorph. United States Patent 5023,092 DuRoss, J.W., 1992. Melt Crystallized Xylitol. United States Patent 5139,795 Gotsis, A.D., Ji, Z., Kalyon, M., 1990. 3-D analysis of the flow in co-rotating twinscrew extruders. Society of Plastics Engineers ANTEC Technical Papers 36, 139– 142. Song, J.H., Townsend, D.J., 1996. Continuous Gum Base Manufacture Using Paddle Mixing. United States Patent 5571543. Yao, C.-H., Manas-Zloczower, I., 1998. Influence of design on dispersive mixing performance in an axial discharge continuous mixer – LCMAX 40. Polymer Engineering and Science 38 (6), 936–946. Zeigler, G.R., Aguilar, C.A., 2003. Residence time distribution in a co-rotating twin screw continuous mixer by the step change method. Journal of Food Engineering 59, 161–167. Zhang, X., Feng, L., Chen, W., Hu, G., 2009. Numerical simulation and experimental validation of mxing performance of kneading discs in a twin screw extruder. Polymer Engineering and Science 49 (9), 1772–1783.