data assimilation for monitoring resin transfer molding … · 2015. 11. 12. · vacuum assisted...
TRANSCRIPT
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7th International Symposium on NDT in Aerospace – Tu.3.A.5
1 License: http://creativecommons.org/licenses/by-nd/3.0/
DATA ASSIMILATION FOR MONITORING RESIN TRANSFER MOLDING OF COMPOSITE
MATERIALS
Ryosuke MATSUZAKI 1, Akira TODOROKI 2, Masayuki MURATA 2, Masaya SHIOTA 1 1 Tokyo University of Science, 2641, Yamazaki, Noda, Chiba, Japan
2 Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro, Tokyo, Japan E-mail address: [email protected] (R. Matsuzaki)
Abstract
Vacuum assisted Resin Transfer Molding (VaRTM) is widely used for molding of composite structures. However, ensuring complete impregnation of the resin into fiber materials is difficult and it sometimes causes the formation of un-impregnated regions, called dry spots. Due to the poor quality of a VaRTM process, its application is currently limited. Therefore, monitoring of the resin flow during the process is necessary to predict and prevent the formation of dry spots. This paper presents a method to observe resin impregnation in a VaRTM process without embedding sensors into composite structures. Planar-shaped sensor electrodes arranged on a molding tool are used to measure electrical capacitance values from pairs of the electrodes. These measurements are combined with the numerical simulations of a VaRTM process to estimate the state of the resin impregnation. This method is based on the ensemble Kalman filter (EnKF), known as a sequential data assimilation technique. The proposed method was examined by a numerical experiment. In the numerical experiment, the resin-impregnated region and the permeability distribution of a fiber preform were estimated concurrently and it was confirmed that the decrease of flow velocity in a low permeability region could be estimated.
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Background
Ø Low cost molding method
Molding tool
GFRP
Dry fabrics Vacuum bag
Molding toolVacuum pumpResin
Resin impregna>on
Dry fabrics 100mm
u VaRTM (Vacuum assisted Resin Transfer Molding)
Monitoring of resin flow is necessary.
Ø Quality problem
Fiber preforms are stacked
Dry spot (Region uncovered with resin)
Embedding sensors in composites may affect on material strength.
Flow direc>on
Op>cal fiber sensor etc.
Measurement range is limited to small area near the sensor.
Measurement instrument
Resis>ve sensor etc.
Resin
Resin inlet
Measurement instrument
Recent studies for flow monitoring
Exis>ng sensors are not suitable for monitoring of thick part processing.
Invasive sensing Non-invasive sensing
2
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Data assimila7on for flow monitoring
non-‐invasive capaci>ve measurements
Stochas>c simula>on of resin flow
Integra>on
u Requirements for flow monitoring of thick part processing
Ø Proposed method: data assimila>on
・ Non-‐invasive sensor ・ Applicability to three dimensional resin flow monitoring
Sequen>al data assimila>on by the Ensemble Kalman Filter
Conflic>ng with each other…
Objec7ves
Development of 3 dimensional resin flow monitoring method by an approach integra>ng sensor measurements and numerical simula>ons
Ø Proposing a sensor that can obtain the informa>on of three dimensional resin flow from a surface of a structure
Ø Developing a method to es>mate resin flow from the measured values and numerical simula>on
Ø Inves>ga>ng the validity of the proposed method by numerical experiments
3
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Overview of the proposed method
Three dimensional resin flow is es>mated.
(1) Capaci>ve sensors
Sequen>al data assimila>on by the (3) Ensemble Kalman Filter
(2) Stochas>c simula>on Uncertainty in a VaRTM process is simulated by
using mul>ple simulators.
u Flow monitoring by an approach integra>ng electrical measurements and numerical simula>ons
(1) Electrical capacitance sensor
A vector ct provides informa>on about 3D resin flow. However, insufficient to reconstruct the resin distribu>on.
Molding tool
Glass fabrics
Electrical capacitance
Electrodes
u Mul>ple electrical capacitance measurements
c1
c2
cM
Resin
Resin distribu>on: N: No. nodesfi :fill frac>on (0≤ fi ≤ 1)
Resin flow represented by f
( )TNt ff ,,1 !=f1
0
0.5
Change with resin flow
Capacitance:M: No. measurements
( )TMt cc ,,1 !=c
Inversion
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(2) Stochas7c Simula7on: Part 1(i) Simula>on of homogeneous model
p∇−=φµKu
Darcy’s law u: Resin velocity, p:Pressure :Porosity, μ:Viscosityφ
(ii) Simula>on of inhomogeneous model
Permeability is spa>ally constant.
Resin
{ })(1)( xKxK α+=Spa>al varia>ons of permeability:
Low High
x: Posi>on
x
z y
Ne: number of finite elements
( )TNe,,, 21 ααα !=αPermeability distribu>on vector
Permeability is not uniformly-‐distributed.
Discre>za>on α(x): Devia>on
K:Preform permeability
(2) Stochas7c Simula7on: Part 2(iii) Stochas>c simula>on of inhomogeneous model
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧ −
−−
−−
−=z
ji
y
ji
x
jiji
zzyyxxCov
ηηησααα exp),(2xx
ηx, ηy, ηz: Correla>on lengths, σα: Spa>al varia>on
⎟⎟⎠
⎞⎜⎜⎝
⎛=
)(0
)(0)(*
0 l
ll
αf
f ft: Resin distribu>on αt: Permeability distribu>on
Ini>al state vectors
α(xi) α(xj)
xzy
Samples of permeability field
Assuming a covariance func>on of the devia>on α(x), samples of spa>ally correlated permeability distribu>on are generated.
1.2
0.8
1.0
1+α{ })(est0)1(est0 ,, Lαα !
),,1( Ll !=
),,1( Ll !=Stochas>c simula>on
)( )*(1)*( l
tl
t F −= ff
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u Darcy’s law
u Con>nuity equa>on u Advec>on equa>on of fill factor
0=⋅∇ u
0)( =⋅∇+∂∂ ftf u
Numerical simulation of VaRTM
⎪⎩
⎪⎨⎧
=ally filled
:Filled
f: fill factor { } { } 0][][ =+ PKfCdtd
u Finite element method
VaRTM simula>on
Computa>on of pressure distribu>on
Update fill factor
Fin.
Ini>al condi>onK: permeability tensor u: velocity, P: pressure : porosity, µ: viscosity
P∇−=φµKu
φ
ft+1true
True resin distribu>on
Δct Measurement
(3) Ensemble Kalman Filter (EnKF)
Ensemble Kalman Filter
ft-‐1*est(1)
ft-‐1*est(L)
Ø Update ft and αt by measurements ct
u Flow monitoring integra>ng simula>on and measurements
ft*fore(1)
ft*est(1)
fttrue
ft+1*fore(1)
t-‐1 t t+1
Δct+1
ft+1*est(1)
Es>ma>onsFiltering
Predic>on
Predictonft*: State vector,
Stochas>c simula>on
)( )(e* 1)(f* l
tl
t F −= ffEs>ma>onForecast
L independent simula>ons
Observa>on equa>on
noise.)( true += tt h fc
h: Observa>on operator St: Sensi>vity matrix vt: Observa>on error vector
!
!
ft-‐1true
tf)f(f )()( vffSf +−+≈ t
lttth
⎟⎟⎠
⎞⎜⎜⎝
⎛=
)(0
)(0)(*
0 l
ll
αf
f
F: Simula>on operator
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Numerical experimentsForward simula>on Es>ma>on by the EnKF
x
zy
Resin inlet
),,1()(*est1 Lll
t !=−f
)( )(*est1)(*fore l
tl
t F −= ff
)( )(estmsr)(*fore)(*est ltttl
tl
t ccGff −+=Gt:Kalman gain
3015 180
Low permeability region, 0.3K0
x
zy
Resin inlet
unit:mm
Glass fabrics, K0K(x)=K0[1+α(x)]
Ini>al ensemble No. members, L=80
1.2
0.8
1.0
1+α
},,{ )(0)1(
0Lαα !
Resin flow:
},,,{
},,,{msrmsr
0
truetrue0
!!
!!
t
t
ccff
u Finite element simula>on
No. elements: 4608 No. nodes: 5625
No. measurements: 36
Ensemble forecast
Update Capacitance:
3015 180
x
z y
unit:mm
(a) Center
(b) Front side
3015 180
x
z y
1.0
0.3
Forward simula>on Es>ma>on by the EnKF
True : fttrue Es>ma>on: Flow front ∑=
=L
l
l
tt L 1)(estest 1 ff
Resin inlet
Results of resin flow es7ma7on: (1)
(a)Center
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1.0
0.3
True : fttrue Es>ma>on: ∑=
=L
l
l
tt L 1)(estest 1 ff
Forward simula>on Es>ma>on by the EnKF
Results of resin flow es7ma7on: (2)
(b)Front side
Resin inlet
Flow frontDecrease in velocity in a low permeability region could be es>mated.
0.3 1.00.4 0.6 0.8
1+α
Results of permeability es7ma7on: (1)Forward simula>on Es>ma>on by the EnKF
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0.3 1.00.4 0.6 0.8
1+α
Results of permeability es7ma7on: (1)
Cross-‐sec>on z=-‐15 mm
Top view (z = -‐15 mm)
Results of permeability es7ma7on: (2)
0.3 1.00.4 0.6 0.8
1+αPermeability distribu>on was es>mated simultaneously.
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Conclusions
Ø Flow monitoring method integra>ng electrical measurements and numerical simula>ons by the EnKF was developed.
Ø In a numerical inves>ga>on, it was confirmed that the resin flow front and permeability field can be es>mated during a VaRTM by the proposed method.
Measurements Simula>on
Bridging the gap between measurements and simulation
Data assimila>on (EnKF)