High Viscous Flow in Silk Spinneret
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High Viscous Flow in Silk Spinneret
2004.May.4th
Tetso Asakura*Ayano Ino*Toshiyuki Suzuki**
* Tokyo University of Agriculture and Technology ** CHAM Japan
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Introduction
For create silk artificially, it is important to application of process of silk spinning.
Silk worm
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Silkworm spinneret
Spinneret
530μm from Spigot
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3D structure silkworm spinneret
Silk
chitin plate
Silk Press part
530m
10m100m
1mm
spigot
Silk tube
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Process of Silk spinning
Silk spinning → “ α to β transition” by shear
Stress
β
Shear Stress
FiberLiquid Protein
α
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Shear rate of Silk fibroin
Experiment of critical shear rate
Kataoka at.al
transition shear rate is
1E+02 ~ 1E-3 sec-1
concentration
Cri
tica
l sh
ear
rate
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Molecular Dynamics simulations
Tensile stress= 0.1GPa
Shear stress=0.3,0.5,0.7,1.0GPa
Conformationalprobability
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Geometry from Biology
Electron microscope
Reconstruct 3D solid
PHOENICS Object
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PHOENICS OBJECTS
■PHOENICS-VR “Objects”
→ Don’t need BFC meshing & Easy to Use
■Complex Geometry
→facet data converted from STL format
■Wall friction added automatically on Object face
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STL(Stereo Lithograph) file
STL file
Solid model ⇒ triangle patchesIt accepts the un-closed and twist
surface Many tools can be used to make it
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Graphical tools to Object( Make STL file from picture)
ElectronMicroscope
1000piecePicture
Reconstruct
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Repair STL
What is required before importing PHOENICS ?
・ No Hole or Gap ・ Surface vector is the same
direction(twist) ・ Cut small parts ・ Smoothing
Repair STL file Cimatron Magics
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Electron Microscopic Repaired by Magics
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Model (meshing)
820μm(nz=205)
156μm (nx=78)
152μ
m (
ny=
78)
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Properties of Silk fibroin
Density 75%water 1.075[g/cm3]
Viscosity Neuton Fluid 6.5E+4[P]
Ref: Water=0.01[P],Glycerin=7.982[P]
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Boundary Conditions
Inlet Velocity 0.178cm/sec(spinneret
velocity=1.0cm/s)
Outlet P=0
Wall Non-Slip
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High Viscosity Flows
Transport Equations∇●u=0
∇●uu= ∇ー p/ρ + μ∇ 2 u
Finite volume equations
ΦP=(aNΦN+aSΦS+etc.)/aP
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Continuity Equations
Error of continuity
R*=cN-cS+etc. c: convective flux
Pressure correction equation
aPpP= aNpN+aSpS+etc.+R*
by default: a=dc/dp
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Convergence acceleration
Pressure correction equation at ADDDIF option for High Viscosity flow
aPpP=aNpN+aSpS+etc.+R*
a=d(c+d)/dp
Diffusion Flux
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Corresponding in MIGAL
MIGAL Solver ⇒ Velocity-Pressure Coupling
ApΦp=ΣAnbΦnb+b
Matrix A included convection and diffusion fluxes
A
x x x
y y y
c c c
u
v
p
b
r
r
r
nb
u
nb
v
nb
p
nb
u
nb
v
nb
p
nb
u
nb
v
nb
p
nb
nb
nb
nb
nb
u
nb
v
nb
p
L
NMMM
O
QPPP
L
NMMM
O
QPPP
L
NMMM
O
QPPP
, ,
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Convergent test
Use cut model near chitin plate
No. of cells =94x114x63
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0.00.10.20.30.40.50.60.70.80.91.0
0 50 100 150 200 250
Time of sweeps[x1000sec]
Flow
rate
Bal
ance
[/]
Orginal
ADDDIF
MIGAL
Flow rate balance=(inlet+outlet)/inlet
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0.E+00
1.E-03
2.E-03
3.E-03
4.E-03
5.E-03
6.E-03
0 50 100 150 200 250
Time of sweeps[x1000sec]
U1
on m
onito
r po
int[
m/s
]
Original
ADDDIF
MIGAL
Monitor value
0.E+00
1.E+05
2.E+05
3.E+05
4.E+05
5.E+05
6.E+05
7.E+05
8.E+05
9.E+05
1.E+06
0 50 100 150 200 250
Time of sweeps[x1000sec]
P1
on m
onito
r po
int[
kPa]
Original
ADDDIF
MIGAL
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0 50 100 150 200 250
Time of sweeps[x1000sec]
W1
on m
onito
r po
int[
m/s
]
Original
ADDDIF
MIGAL
Pressure
Z Velocity
X Velocity
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1.E+06
1.E+07
1.E+08
1.E+09
1.E+10
1.E+11
1.E+12
0 50 100 150 200 250
Time of sweeps[x1000sec]
Res
idua
l of P
1ADDDIF
MIGAL
1.E+13
1.E+14
1.E+15
1.E+16
1.E+17
1.E+18
1.E+19
1.E+20
0 50 100 150 200 250
Time of sweeps[x1000sec]R
esid
ual o
f W1
ADDDIF
MIGAL
1.E+13
1.E+14
1.E+15
1.E+16
1.E+17
1.E+18
0 50 100 150 200 250
Time of sweeps[x1000sec]
Res
idua
l of U
1
ADDDIF
MIGAL
ResidualPressure
Z Velocity
X Velocity
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Pressure and Velocity
Pressure[kPa] Streamline[msec]
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Slip velocities(shear rate)
In PHOENICS, the magnitude of the total rate of strain GEN1 is given as,
GEN1=2*[(du/dx)2+(dv/dy)2+(dw/dz)2] +(du/dy+dv/dx)2
+(dv/dz+dw/dy)2
+(dw/dx+du/dz)2
Slip velocity is Vs=SQRT(GEN1)
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Slip Velocities of cross section [1/sec]
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Summary & Conclusion
About Simulation Result The maximum shear velocities is
45[1/s] at silk press part. Where is provided the transition from liquid protein to fiber.
Static Pressure loss is Giga Pascal order in spinner. It is as same as the transition stress with the molecular dynamics simulation.
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Summary & Conclusion 2
About CFD technique With some graphical tools, we can
calculate easily the case with complex biology geometry by PHOENICS.
A better convergence has been gotten by adding the diffusion velocity into pressure correction equation for High Viscous Flow, If we desire much better performance, we can use MIGAL.
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Summary & Conclusion 3
Future and next step PARSOL (Cut cell) Pressing at chitin plate (use Moving Grid
or MOFER). Survey for the fibroin properties.