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

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 1

Problem Statement Estimate the whole-field permeability with local variations based on the given pressure profile and the fiber volume measured Fiber volume pressure profile Model + Algorithm Darcy’s law whole-field permeability estimation Methodology Irrotational + Incompressible Δϕ = 0 Darcy’s law + Incompressible Boundary Boundary conditions ∇ ⋅ ( k ∇ P )=0 Computed Initial K pressure Boundary conditions + Incremental Heuristic Adaptive Nonlinear Optimization N No Measured Match converges ? pressure Yes Output K 2

Experimental Setup of GRASP-RTM upper mold Injection p pressure: ≈ 0.14psi Fiber preform Inlet and flowmeter Outlet and flowmeter Control valve at inlet Computer Lower mold and pressure sensor array Gas N 2 nitrogen gas μ = 1.78 × 10 -5 Pa.s(kg/m.s) Data acquisition board Circuit board Experimental Setup of GRASP-RTM (Cont’d) GRASP Testbed Pressure sensors connection Lower section of the mold Mold cavity 3

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 4

Experimental Setup of GRASP-RTM (Cont’d) Fiber preform Data Acquisition and Processing Calibration averaging Measured Pressure values at discrete locations Data acquisition 5

Data Acquisition and Processing (Cont’d) Acquire continuous image of measured pressure profile of regular mold geometry by linear interpolation P i+1,j+1 P i,j+1 P 3 y j+1 (x,y) P 4 P 2 P y j P i,j P i+1,j P 1 x i x i+1 − + − + − + − ( ) ( ) ( ) ( ) P y y P y y P x x P x x + + = 1 j 1 3 j 2 i 1 4 i P − + − x x y y + + i 1 i j 1 j Interpolation Measured pressure profile Data Acquisition and Processing (Cont’d) Acquire continuous image of measured pressure profile of irregular mold geometry by Gibbs sampling ∈ ⎧ P ( x , y ) N [( x , y )]; ⎪ ij i j ( 0 ) = ( , ) ⎨ P x y ∉ 0 ( , ) U [( , ) m x y N x y ⎪ ⎩ i j , all i j ⎧ ∈ ( , ) [( , )]; P x y N x y ⎪ ij i j ( ) = t ⎨ P ( x , y ) ∉ m P ( x , y ) U N [( x , y ) ⎪ ⎩ i j all i , j ∈ ( t ) P ~ f ( P ( x , y ) | P ( x , y ) : ( x , y ) S ( t ) m m − ∉ ( t 1 ) P ( x , y ) : ( x , y ) S ( t )) m f ( p ( x , y )) = N ( , σ 2 ) f ( ( )) N ( 2 ) P P ( ( x , y ) ) ∫∫ ⋅ P ( x , y ) dxdy = N [( x , y )] ( , ) P x y ∫∫ dxdy N [( x , y )] Gibbs sampling Measured pressure profile 6

Reynolds Number ρ ρ ⋅ k ∇ ⋅ ∇ ⋅ k P P d d • according to the fluid mechanics according to the fluid mechanics = f f 2 Re μ 2 theory, when the Reynolds number (Re) is sufficiently small ∇ P is the pressure gradient (preferably less than 0.1), the field of the steady gas flow effects of the compressible and ρ =1.2 (kg/m 3 ) is the density inertial behaviors of fluid can be of the gas neglected, and the laminar or d f =5.51 × 10 -4 (in) (1.40 × 10 -5 m) creeping flow mechanism remains p g is the diameter of the fiber μ = 1.78 × 10 -5 Pa.s(kg/m.s) is within the flow field. the viscosity of the nitrogen gas Results of GRASP-RTM Finite element analysis Finite element analysis Measured pressure profile Measured pressure profile (Pa.) 3D plot Contour Reynolds number profile in case 1 Computed pressure profile Relative error profile (Pa.) Pressure match in case 1 (maximum relative error at a node: 0.0059) Reynolds mean max min number 0.0302 0.0664 0.0106 3D plot permeability mean max min Contour (m 2 ) Permeability (m 2 ) profile estimation of case 1 3.16e-010 4.69e-009 3.86e-011 7

Results of GRASP-RTM (Cont’d) Finite element analysis Measured pressure profile (pa ) (pa.) 3D plot Contour Reynolds number profile in case 2 Computed pressure profile Relative error profile (Pa.) Pressure match in case 2 (maximum relative error at a node: 0.0096 ) Reynolds mean max min number 0.0347 0.0753 8.84e-004 3D plot permeability mean max min Contour (m 2 ) Permeability (m 2 ) profile estimation of case 2 3.26e-010 5.61e-009 2.62e-011 Results of GRASP-RTM (Cont’d) Finite element analysis Measured pressure profile (Pa.) 3D plot Contour Reynolds number profile in case 3 Computed pressure profile Relative error profile (Pa.) Pressure match in case 3 (maximum relative error at a node: 0.0055 ) Reynolds mean max min number 0.0210 0.0415 5.9546e-004 3D plot Contour permeability mean max min Permeability (m 2 ) profile estimation of case 3 (m 2 ) 3.10e-010 3.40e-009 4.13e-011 8

Results of GRASP-RTM (Cont’d) Finite element analysis Measured pressure profile (Pa ) (Pa.) 3D plot Contour Reynolds number profile in case 4 Computed pressure profile Relative error profile (Pa.) Pressure match in case 4 (maximum relative error at a node: 0.0032 ) Reynolds mean max min number 0.0195 0.0797 6.07e-04 3D plot Contour permeability mean max min Permeability (m 2 ) profile estimation of case 4 (m 2 ) 3.14e-010 4.36e-009 3.00e-011 Experimental Setup of GRASP-VARTM Data acquisition board Circuit board Computer Vacuum Vacuum pressure: pressure: ≈ -xxx psi ≈ -xxx psi air upper film and μ = 1.73 × 10 -5 Pa.s(kg/m.s) pressure sensor array Inlet and Outlet and flowmeter flowmeter Lower mold Fiber preform Control valve at outlet Control valve at inlet Vacuum pump Schematic of experimental setup 9

Experimental Setup of GRASP-VARTM (Small Part: 9 × 6 in 2 ) Apparatus Fiber loading ( V f ≈ 43%) Mold design Pressure sensors installing Vacuum test Experimental Setup of GRASP-VARTM (Large Part: 20.5 × 20 in 2 ) Apparatus Pressure sensors installing Mold design Fiber loading( V f ≈ 43%) and vacuum test 10

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 Calibration averaging Measured values of Pressure difference at discrete locations Data acquisition 11

Data Acquisition and Processing (Cont’d) Acquire continuous image of measured pressure profile of regular mold geometry by linear interpolation P i+1,j+1 P i,j+1 P 3 y j+1 (x,y) P 4 P 2 P y j P i,j P i+1,j P 1 x i x i+1 − + − + − + − ( ) ( ) ( ) ( ) P y y P y y P x x P x x + + = = 1 j 1 3 j 2 i 1 4 i P P − + − x x y y + + i 1 i j 1 j Pressure difference Pressure Interpolation Measured pressure profile Geometric Description ( Small Part: 9 × 6 in 2 ) 3-D geometric description of Finite element analysis of the the fiber preform fiber preform geometry 12

Geometric Description ( Large Part : 20.5 × 20 in 2 ) 3-D geometric description of Finite element analysis of the the fiber preform fiber preform geometry Data Processing and Results ( Small Part) Slice data collected by pressure sensors Slice data collected by pressure sensors (9 slices along x-directon) (6 slices along y-directon) 13

Data Processing and Results ( Small Part, Cont’d) Estimation of permeability profile (m 2 ) pressure profile obtained by interpolation Pressure at Inlet Outlet permeability mean max min inlet and outlet (m 2 ) 3.310e-010 2.157e-009 1.200e-011 (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 14

Data Processing and Results ( Large Part) Slice data collected by pressure sensors Slice data collected by pressure sensors (8 slices along x-directon) (8 slices along y-directon) Data Processing and Results ( Large Part, Cont’d) Estimation of permeability profile (m 2 ) pressure profile obtained by interpolation Pressure at Inlet Outlet permeability mean max min inlet and outlet (m 2 ) 3.887e-010 3.254e-008 2.010e-011 (Kpa) -30.17 -33.99 15

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) Vent Gate 3 ( auxiliary gate ) Gate 2 ( auxiliary gate ) G ( y g ) Gate 1 ( main gate ) Establishment of auxiliary gates Experimental setup and vacuum test 16