Abstract Developed an effective 2D and 3D numerical Developed an - - PDF document

1 Three Dimensional Permeability Estimation for RTM and VARTM Processes

Xugang Ye

Department of Industrial and Manufacturing Engineering Florida State University

Abstract

• Developed an effective 2D and 3D numerical

Developed an effective 2D and 3D numerical methods for estimating whole-field permeability profile with local variations from measured pressure profile and given fiber volume

• Set up the GRASP-RTM and GRASP-VARTM

testbeds for experimental validation of 2D and 3D p whole-field permeability estimation in RTM and VARTM processes

2

Problem Statement

Estimate the whole-field permeability with local variations based on the given pressure profile and the fiber volume

measured pressure profile Fiber volume Model + Algorithm Darcy’s law whole-field permeability estimation

Methodology

Boundary

Δϕ = 0

Darcy’s law + Incompressible Irrotational + Incompressible

Initial K

+

Boundary conditions

∇ ⋅ ( k ∇ P )=0

Boundary conditions Computed pressure Adaptive Nonlinear Optimization

Incremental Heuristic

N Match converges ? No Yes Output K Measured pressure

3

Experimental Setup of GRASP-RTM

upper mold

Injection pressure:

Fiber preform Lower mold and pressure sensor array Inlet and flowmeter Outlet and flowmeter N 2 Gas Computer

p ≈ 0.14psi

Control valve at inlet Circuit board Data acquisition board

nitrogen gas μ = 1.78×10-5 Pa.s(kg/m.s)

Experimental Setup of GRASP-RTM (Cont’d)

GRASP Testbed Pressure sensors connection Mold cavity Lower section of the mold

4

Experimental Setup of GRASP-RTM (Cont’d)

0/90 balanced knitted E-glass fabrics (COFAB A118 Collins fabrics (COFAB A118, Collins Craft Composites Inc., Walhalla, SC) Average permeability against fiber volume

Experimental Setup of GRASP-RTM (Cont’d)

Fiber preform

5

Experimental Setup of GRASP-RTM (Cont’d)

Fiber preform

Data Acquisition and Processing

averaging Calibration

Measured Pressure values at discrete locations

Data acquisition

6

Data Acquisition and Processing (Cont’d)

Acquire continuous image of measured pressure profile of regular mold geometry by linear interpolation

Pi,j+1 Pi+1,j+1 Pi+1,j Pi,j P1 P3 P2 P4 P

(x,y)

yj+1 yj xi+1 xi

Measured pressure profile Interpolation

j j i i i i j j

y y x x x x P x x P y y P y y P P − + − − + − + − + − =

+ + + + 1 1 4 1 2 3 1 1

) ( ) ( ) ( ) (

Data Acquisition and Processing (Cont’d)

Acquire continuous image of measured pressure profile of irregular mold geometry by Gibbs sampling

⎪ ⎩ ⎪ ⎨ ⎧ ∉ ∈ = ) , [( ) , ( )]; , [( ) , ( ) , (

, ) ( j i j i all j i ij m

y x N y x y x N y x P y x P U ⎪ ⎩ ⎪ ⎨ ⎧ ∉ ∈ = ) , [( ) , ( )]; , [( ) , ( ) , (

, ) ( j i j i all j i ij t m

y x N y x P y x N y x P y x P U )) ( ) , ( : ) , ( ) ( ) , ( : ) , ( | ) , ( ( ~

) 1 ( ) (

t S y x y x P t S y x y x P y x P f P

t m t m m

∉ ∈

−

f ( ( )) N (

2)

) ( P

Measured pressure profile Gibbs sampling

f (p(x,y)) = N ( , σ2) ) , ( y x P

∫∫ ∫∫

⋅ =

)] , [( )] , [(

) , ( ) , (

y x N y x N

dxdy dxdy y x P y x P

7

Reynolds Number

according to the fluid mechanics

ρ

f

d P k ⋅ ∇ ⋅ ⋅

• according to the fluid mechanics

theory, when the Reynolds number (Re) is sufficiently small (preferably less than 0.1), the effects of the compressible and inertial behaviors of fluid can be neglected, and the laminar or creeping flow mechanism remains

2 2

Re μ ρ

f

d P k ∇ =

∇ P is the pressure gradient field of the steady gas flow ρ =1.2 (kg/m3) is the density

• f the gas

df =5.51×10-4(in) (1.40×10-5m) is the diameter of the fiber

p g within the flow field.

μ = 1.78×10-5 Pa.s(kg/m.s) is the viscosity of the nitrogen gas

Results of GRASP-RTM

Finite element analysis Measured pressure profile

Pressure match in case 1 (maximum relative error at a node: 0.0059)

Finite element analysis Measured pressure profile (Pa.) Computed pressure profile (Pa.) Relative error profile

Reynolds number profile in case 1

3D plot Contour

Permeability (m2 ) profile estimation of case 1 permeability mean max min (m2 ) 3.16e-010 4.69e-009 3.86e-011

3D plot Contour

Reynolds mean max min number 0.0302 0.0664 0.0106

8

Results of GRASP-RTM (Cont’d)

Finite element analysis Measured pressure profile (pa )

Pressure match in case 2 (maximum relative error at a node: 0.0096)

(pa.) Computed pressure profile (Pa.) Relative error profile

Reynolds number profile in case 2

3D plot Contour

Permeability (m2 ) profile estimation of case 2 permeability mean max min (m2 ) 3.26e-010 5.61e-009 2.62e-011

3D plot Contour

Reynolds mean max min number 0.0347 0.0753 8.84e-004

Results of GRASP-RTM (Cont’d)

Finite element analysis Measured pressure profile

Pressure match in case 3 (maximum relative error at a node: 0.0055)

(Pa.) Computed pressure profile (Pa.) Relative error profile

Reynolds number profile in case 3

3D plot Contour

Permeability (m2 ) profile estimation of case 3 permeability mean max min (m2 ) 3.10e-010 3.40e-009 4.13e-011

3D plot Contour

Reynolds mean max min number 0.0210 0.0415 5.9546e-004

9

Results of GRASP-RTM (Cont’d)

Finite element analysis Measured pressure profile (Pa )

Pressure match in case 4 (maximum relative error at a node: 0.0032)

(Pa.) Computed pressure profile (Pa.) Relative error profile

Reynolds number profile in case 4

3D plot Contour

Permeability (m2 ) profile estimation of case 4 permeability mean max min (m2 ) 3.14e-010 4.36e-009 3.00e-011

3D plot Contour

Reynolds mean max min number 0.0195 0.0797 6.07e-04

Experimental Setup of GRASP-VARTM

air μ = 1.73×10-5 Pa.s(kg/m.s)

Data acquisition board Computer Circuit board upper film and pressure sensor array

Vacuum pressure: ≈ -xxx psi Vacuum pressure: ≈ -xxx psi

Schematic of experimental setup

Inlet and flowmeter Outlet and flowmeter Fiber preform Lower mold Control valve at inlet Control valve at outlet Vacuum pump

10

Experimental Setup of GRASP-VARTM (Small Part: 9 × 6 in2 )

Mold design Fiber loading ( Vf≈43%)

Apparatus

Vacuum test Pressure sensors installing

Experimental Setup of GRASP-VARTM (Large Part: 20.5 × 20 in2 )

Apparatus

Pressure sensors installing Mold design Fiber loading( Vf≈43%) and vacuum test

11

Experimental Setup of GRASP-VARTM (Cont’d)

0/90 balanced knitted E-glass fabrics (COFAB A118 Collins fabrics (COFAB A118, Collins Craft Composites Inc., Walhalla, SC) Average permeability against fiber volume

Data Acquisition and Processing

averaging Calibration

Measured values of Pressure difference at discrete locations

Data acquisition

12

Data Acquisition and Processing (Cont’d)

Acquire continuous image of measured pressure profile of regular mold geometry by linear interpolation

Pi,j+1 Pi+1,j+1 Pi+1,j Pi,j P1 P3 P2 P4 P

(x,y)

yj+1 yj xi+1 xi

i i j j

x x P x x P y y P y y P P − + − + − + − =

+ + 4 1 2 3 1 1

) ( ) ( ) ( ) ( Measured pressure profile

Interpolation

j j i i

y y x x P − + − =

+ + 1 1

Pressure difference Pressure

Geometric Description (Small Part: 9 × 6 in2 )

3-D geometric description of the fiber preform Finite element analysis of the fiber preform geometry

13

Geometric Description (Large Part : 20.5 × 20 in2 )

3-D geometric description of the fiber preform Finite element analysis of the fiber preform geometry

Data Processing and Results

(Small Part)

Slice data collected by pressure sensors (9 slices along x-directon) Slice data collected by pressure sensors (6 slices along y-directon)

14

Data Processing and Results

(Small Part, Cont’d)

pressure profile obtained by interpolation Estimation of permeability profile (m2 )

permeability mean max min (m2 ) 3.310e-010 2.157e-009 1.200e-011

Pressure at inlet and outlet

Inlet Outlet (Kpa)

• 32.89
• 33.98

Experiment V.S Simulation (Small Part)

Video captures of the experiments Simulation of filling process under the measured permeability profile

15

Data Processing and Results

(Large Part)

Slice data collected by pressure sensors (8 slices along x-directon) Slice data collected by pressure sensors (8 slices along y-directon)

Data Processing and Results

(Large Part, Cont’d)

pressure profile obtained by interpolation Estimation of permeability profile (m2 )

permeability mean max min (m2 ) 3.887e-010 3.254e-008 2.010e-011

Pressure at inlet and outlet

Inlet Outlet (Kpa)

• 30.17
• 33.99

16

Experiment V.S Simulation (Large Part)

Video captures of the experiments

Final state

Simulation of filling process under the measured permeability profile

More Results of Large Part (Multigates)

Gate 2 ( auxiliary gate ) Gate 3 ( auxiliary gate ) Vent

Establishment of auxiliary gates Experimental setup and vacuum test

G ( y g ) Gate 1 ( main gate )

17

More Results of Large Part (Multigates, Cont’d)

pressure profile obtained by interpolation Estimation of permeability profile (m2 )

permeability mean max min (m2 ) 3.905e-010 3.799e-008 1.780e-011

Pressure at inlet and outlet

Inlet (1,2,3) Outlet (Kpa)

(-30.15, -30.93, -30.88)

• 33.94

Experiment V.S Simulation (Large Part , Cont’d)

Video captures of the experiments

Final state

Simulation of filling process under the measured permeability profile

18

Experiment V.S Simulation (Large Part , Cont’d)

Video captures of the experiments

Final state

Simulation of filling process under the measured permeability profile

Final state

Conclusions

• In-situ, whole-field permeability measurement

In situ, whole field permeability measurement using gas is advantageous

• GRASP can detect typical fiber preform defects

qualitatively and quantitatively in RTM and VARTM processing

• Combined with flow simulation, GRASP can

provide an effective tool for RTM and VARTM process design and control

19

Acknowledgment

• The work has been supported by Army Research

The work has been supported by Army Research Lab, GKN Aerospace Services, National Science Foundation, Office of Naval Research and CAPCE members

Questions?

20

Thanks very much!