Transcript High Viscous Flow in Silk Spinneret

High Viscous Flow
in Silk Spinneret
2004.May.4th
Tetso Asakura*
Ayano Ino*
Toshiyuki Suzuki**
* Tokyo University of Agriculture and Technology
** CHAM Japan
Introduction
For create silk artificially, it is important to
application of process of silk spinning.
Silk worm
Silkworm spinneret
530μm from Spigot
Spinneret
3D structure silkworm spinneret
Silk Press part
chitin
plate
Silk
530
m
1mm
spigot
Silk tube
10m
100m
Process of Silk spinning
Silk spinning
→ “α to β transition” by shear Stress
Shear Stress
α
Liquid Protein
β
Fiber
Shear rate of Silk fibroin
Experiment of critical shear rate
Critical shear rate
Kataoka at.al
transition shear rate is
1E+02～1E-3 sec-1
concentration
Molecular Dynamics simulations
Tensile stress
=0.1GPa
Shear stress
=0.3,0.5,0.7,1.0GPa
Conformational
probability
Geometry from Biology
Electron microscope
Reconstruct 3D solid
PHOENICS Object
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
STL(Stereo Lithograph) file
STL file
Solid model ⇒ triangle patches
It accepts the un-closed and twist surface
Many tools can be used to make it
Graphical tools to Object
（Make STL file from picture)
Electron
Microscope
Reconstruct
1000piece
Picture
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
Electron Microscopic
Repaired by Magics
152μm (ny=78)
Model (meshing)
820μm
(nz=205)
156μm (nx=78)
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]
Boundary Conditions
Inlet Velocity
0.178cm/sec
(spinneret velocity=1.0cm/s)
Outlet
P=0
Wall
Non-Slip
High Viscosity Flows
Transport Equations
∇●u=0
∇●uu= ー∇p/ρ ＋ μ∇２u
Finite volume equations
ΦP=(aNΦN+aSΦS+etc.)/aP
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
Convergence acceleration
Pressure correction equation at ADDDIF option
for High Viscosity flow
aPpP=aNpN+aSpS+etc.+R*
a=d(c+d)/dp
Diffusion Flux
Corresponding in MIGAL
MIGAL Solver ⇒ Velocity-Pressure Coupling
ApΦp=ΣAnbΦnb+b
L
x
M
AM
y
M
c
N
u
nb
x
u
nb
ynbv
ynbp
u
nb
v
nb
p
nb
c
v
nb
x
c
p
nb
O
P
,
P
P
Q
L
u O
r O
L
M
P
M
P
M
v P , b  M
r P
M
P
M
P

p
r
N Q NQ
u
nb
nb
v
nb
nb
nb
p
nb
nb
Matrix A included convection and diffusion fluxes
Convergent test
Use cut model near
chitin plate
No. of cells
=94x114x63
Flowrate Balance[/]
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Orginal
ADDDIF
MIGAL
0
50
100
150
200
250
Time of sweeps[x1000sec]
Flow rate balance=(inlet+outlet)/inlet
Monitor value
1.E+06
P1 on monitor point[kPa]
9.E+05
Pressure
8.E+05
7.E+05
6.E+05
Original
5.E+05
ADDDIF
4.E+05
MIGAL
3.E+05
2.E+05
0.014
1.E+05
0
50
100
150
Time of sweeps[x1000sec]
200
U1 on monitor point[m/s]
6.E-03
5.E-03
W1 on monitor point[m/s]
0.012
0.E+00
250
0.010
Original
0.008
ADDDIF
0.006
MIGAL
0.004
Z Velocity
0.002
0.000
0
4.E-03
Original
ADDDIF
3.E-03
MIGAL
2.E-03
X Velocity
1.E-03
0.E+00
0
50
100
150
Time of sweeps[x1000sec]
200
250
50
100
150
Time of sweeps[x1000sec]
200
250
Residual
Pressure
1.E+12
1.E+11
Residual of P1
ADDDIF
1.E+10
MIGAL
1.E+09
1.E+08
1.E+07
50
100
150
200
Time of sweeps[x1000sec]
250
X Velocity
1.E+18
1.E+17
ADDDIF
1.E+16
MIGAL
1.E+15
1.E+14
1.E+13
0
50
100
150
200
Time of sweeps[x1000sec]
250
1.E+19
Residual of W1
0
Residual of U1
Z Velocity
1.E+20
1.E+06
1.E+18
ADDDIF
1.E+17
MIGAL
1.E+16
1.E+15
1.E+14
1.E+13
0
50
100
150
200
Time of sweeps[x1000sec]
250
Pressure and Velocity
Pressure[kPa]
Streamline[msec]
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)
Slip Velocities of cross section [1/sec]
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.
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.
Summary & Conclusion 3
Future and next step
PARSOL (Cut cell)
Pressing at chitin plate (use Moving Grid or
MOFER).
Survey for the fibroin properties.