Fill ratio distribution in a co-rotating self-wiping twin screw extruder theoretical and experimental study

Transcription

1 8:00-8:30am 30 min. Fill ratio distribution in a o-rotating self-wiping twin srew extruder theoretial and experimental study Kentaro Taki, Kanazawa University, Kanazawa, Ishikawa, Japan, Shin-ihiroTanifuji, HASL, Tokyo, Japan, Takemasa Sugiyama, Kanazawa University, Kanazawa, Ishikawa, Japan Jun-ihiMurata, Kaneka, Osaka, Japan, Isao Tsujimura, Kaneka, Osaka, Japan 1

2 Agenda 1. Introdution 2. Theory and formulation 3. Algorithm for fill ratio distribution 4. Conlusion 2

3 Numerial Simulation of TSE Resolution FAN method This study [3] 3D sim et [1] [2] 1 s 1-10 min 1 day-1 week Calulation time 1. Yasuya Nakayama, Toshihisa Kajiwara, Tatsunori Masaki, AIChE J, 62(7), (2016).b 2. Andreas Eitzlmayr, Johannes Khinast, Chemial Engineering Siene, 134, (2015). 3. Tadmor, Z., Broyer, E. and Gutfinger, C.: Polym. Eng. Si., 14,660(1984) 4. Broyer, E., Gutfinger, C. and Tadmor Z. : Trans. So. Rheology, 19, 423(1975) 5. J. L. White, Z. Y. Chen, Polymer Engineering and Siene, 34(3), (1994). 6. Santosh Bawiskar, James L. White, Polymer Engineering & Siene, 38(5), (1998). 7. James L. White, EungKyuKim, Jong Min Keum, Ho ChulJung, DaeSuk Bang, (C)Kentaro Polymer Engineering Taki, Kanazawa & Siene, University 41(8), (2001). 8. J. L. White, B. J. Kim, S. Bawiskar, J. M. Keum, Polymer-Plastis Tehnology and Engineering, 40(4), (2001). 3

4 What our simulator an do. Hele-Shaw flow model + finite element method Pressure distribution Fill ratio distribution Strain rate, veloity, flow rate distribution on whole srew elements Strain magnitude Droplet dispersion Fiber attrition Plastiization 4

5 Advantage of our software 1. Calulation ost is low as the pressure is the only unknown variable to be determined for isothermal ondition. 2. It is easy to alulate flow metris; veloity, strain rate, visosity distribution by the integration along the thikness (r diretion) when the pressure and temperature are determined. 3. Flow balane satisfies with high-preision. Q 4 Q 3 Element Q Q 1 2 q 4 q 3 q 1 q 2 Internal node The total flow rate at a node beomes zero for any values of pressure. The summation of flow rate for internal nodes alulated by the pressure beomes zero. 4 Q 4 0 Q φ α α 1 α 1 4 q α α 1 α 0 1 5

6 Hele-Shaw flow 2.5D model in ylinder Ω v r 0, v z and v are solo funtion of r. v 0, v 0 at r b z R s v R Ω, v 0 at r z R b R b R s r z R s : Srew radius R b : Barrel radius 6

7 Geometry 7

8 Shape funtion p φ p φ z φ z r R R ζ + R,,, ( ) b s L s α α α α α α α 1 α 1 α φ1 ξl ηl φ2 + ξl ηl φ3 + ξl + ηl φ4 ξl + ηl ( 1 )( 1 ), ( 1 )( 1 ), ( 1 )( 1 ), ( 1 )( 1 ) Element in ylindrial oordinate Element in omputational oordinate 8

9 Eq. of Continuity in ylindrial oordinate As ρ onstant and v r 0, ρ ( ρ rv ) ( ) ( ) r + ρ v + ρ vz t r r r z 0 1 r ρ v + ρ v z z ( ) ( ) 0 9

10 -omponent Eq. of Motion As steady state, v / v /z 0, v r 0, 2 2 η η v v 2 v 1 ( ) η r p rv + η r r r r z r r 1 v v 1 p r η 2 2 r r r r r 10

11 z-omponent Eq. of Motion (Cont ) As steady state, v z / v z /z 0, v v v p + + r r r r z z 1 2 η rη z z η z v p rη r r r z 1 z 11

12 r-omponent zr-omponent & γ r & γ zr Integration onstant Strain rate v 1 p 1 1 Ω Ω r 1 r r η r γ η r γ vz 1 p 1 α r z 2η z r β 3 α Rb r Rb 1 Rb 1 Rb r dr, β dr, dr, R 3 dr s Rs r γ η η Rs ηr δ R s η 12

13 Veloity -omponent z-omponent r p r 1 β r 1 r Ωr 1 v dr dr + dr Rs ηr γ Rs Rs ηr γ ηr 1 p r r α r 1 vz dr dr 2 z Rs η β Rs ηr Integration onstant 3 α Rb r Rb 1 Rb 1 Rb r dr, β dr, dr, R 3 dr s Rs r γ η η Rs ηr δ R s η 13

14 Flow rate -omponent 2 Rb 1 p β Ω 2 β q v dr R α + Rb s 4 γ 2 γ z-omponent q 2 Rb 1 p α v rdr δ Rs 4 z β z z Integration onstant 3 α Rb r Rb 1 Rb 1 Rb r dr, β dr, dr, R 3 dr s Rs r γ η η Rs ηr δ R s η 14

15 Flow balane of eah element 15 ( ) e e ez e e D p S S Q α β αβ αβ α + + ds D D ds z z S S ds S S d q n q n Q e e e e S e S z ez S e z z e Γ + Γ φ φ φ φ φ φ α α β α αβ β α αβ α α,,, ) ( dr r dr r dr r dr r b s b s b s b s R R R R R R R R η δ η γ η β η α 3 3, 1, 1, Ω b z R D S S γ β β α δ γ β α , 4 1, 4 1 Flow through a node of element Pressure-gradient driven flow Drag-fore driven flow ( )( ) ( )( ) ( )( ) ( )( ) , 1 1, 1 1, L L L L L L L L φ ξ η φ ξ η φ ξ η φ ξ η

16 Filled and unfilled alulation Completely filled srews Press. at feed 0MPa(given) Press. at feed 0MPa(given) Press. at feed 0MPa(given) Partially filled srew Head press. 10MPa(given) Q 20kg/h (Cal. result) Head press. 5MPa(given) Q 40kg/h (Cal. result)? Q 20kg/h(given) One degree of freedom is added. Head press. 5MPa(given) 16

17 Pressure downstream update sheme Srew inlet position Srew head position Z :Element to be renew 1 st step pressure distribution :Downstream elements f1.0 f0 Correted pressure distribution Filling ratio distribution Z Z Pressure downstream update sheme p p p ( z z, ) p( z, ) z z As the pressure is need to be determined aording to the two oordinates (z, ), the pressure downstream update sheme is developed. FAN method (1D) 2.5D FEM 17

18 Criteria of filled and unfilled Pressure gradient Flow balane Pressure Fill or Unfill dp/dx<0 Q>Q d p>0 Filled 1) f e 1 dp/dx>0 Q<Q d p>0 Filled 2) f e 1 dp/dx>0 Q<Q d p<0 p0 Unfilled 3) f e 0 1) Q>Q d, unfilled state is impossible. 2) Q<Q d, p>0 : Filled sate and bak flow (pressure gradient driven flow) is larger than the net flow. 3) Q<Q d, p<0 : Unfilled state and orretion of p0,wfwareapplied for FAM method (fq/q d ). Q WVb H 4 3 WH sin(2 ) 12η dp dx Drag-fore driven flow Q d Pressure gradient driven flow,q p 18

19 Corretion of pressure distribution Fill ratio ontrol line Z f Average fill ratio determined by pressure distribution av V e e V f e Q ext z-axis fill ratio determined by srew geometry Q z d V D f α D z ave d α osφ sinφ XH X Z sinφ osφ Q ext z Qd Adjusting pressure distribution to agree f av with f z. 19

20 180 C 190 C 200 C Performing simulation Simple wizard for onstruting srew geometry Automati meshing Complex visosity [Pa s] E Strain rate [s -1 ] Visosity-strain rate model e.g., Cross model Operation variables (Feed rate, Q, Head pressure P, Rot speed N) Calulation of pressure distribution by FEM. Fill ratio distribution 20

21 Effet of Srew Speed (rpm) Fill ratio Un-filled Filled Feed rate 0.75kg/h 100 rpm head 50 rpm 30 rpm Derease of srew speed expands filled region bakwards. 21

22 Effet of feed rate (kg/h) Fill ratio Un-filled Filled Speed 30 rpm 0.25 kg/h 0.50 kg/h 0.75 kg/h Inrease of feed rate expands filled region bakwards. 22

23 Experiments Material Homo polypropylene (F-704NP, Prime Polymer, Japan) Visosity-strain rate urve was obtained by the Cross model Complex visosity [Pa s] Cross model 180 C 190 C 200 C 100 1E ( &, T, P) η γ 1 η η & γ τ 0 + * T b 1 η0 a exp T Strain rate [s -1 ] 23

24 Srew geometry and barrel temp. Self-wiping o-rotating parallel twin srew extruder L/D 90, φ 15 mm (Tehnovel, Japan) 24

25 30 rpm 0.5 kg/h Fill ratio Fill ratio distribution Low (0) High (1) Pulled-out srew Simulation 25

26 Srew speed (rpm) vs. Fill ratio 0.3 Fill ratio [-] x0.5 Cal. The alulation results agree with the theoretial definition, Q/Q d as the fill ratio beame half when the srew speed beomes double. x Srew rotational speed [rpm] 26

27 Feed rate vs. fill ratio Fill ratio [-] Calulation agrees with the theoretial definition of fill ratio, Q/Q d as the plots exist on the straight line from origin. 0.1 Cal Feed rate [kg/h] 27

28 Throughput vs. fill ratio Fill ratio [-] Cal. Calulation agrees with the theoretial definition of fill ratio, Q/Q d as the plots exist on the straight line from origin Feed rate and Rotational spped ratio, Q/N [kg/(h rpm)] 28

29 Conlusion We ahieved a development of 2.5D Hele-Shaw model for alulation of pressure distribution in twin srew extruder. This model has advantage for short-alulation time, possible to whole srew elements. The fill ratio was alulated based on the FAN method. Further experimental validations not only the fill ratio but also fiber attrition, plastiization et are demanded. Devolatilization model will be added. 29

30 Contat information This software is proprietary and ommerially available by the HASL Co. ltd., Japan. Please ontat Dr. Shin-ihiro Tanifuji, CEO of HASL. URL: Thank you for your kind attention. CEO Dr. Shin-ihiro Tanifuji 30