Numerical Sensitivity Analysis of a complex Glass Forming Process by means of local perturbations

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Bernard, Hannes Birkenhofer Fraunhofer Institute of Optronics,

1 Numerical Sensitivity Analysis of a complex Glass Forming Process by means of local perturbations Chettapong Janya-anurak, Thomas Bernard, Hannes Birkenhofer Fraunhofer Institute of Optronics, System Technologies and Image Exploitation Karlsruhe, Germany Fraunhofer IOSB 1

Motivation: Glass forming Process Industrial glass forming batch process Resulting

(precise diameter and wall thickness) Blowing pressure pressure Challenges: highly

2 Motivation: Glass forming Process Industrial glass forming batch process Resulting tubes / rods are pre-product for optical fibers Very high quality requirements (precise diameter and wall thickness) Blowing pressure pressure Challenges: highly nonlinear process radiation material properties strong disturbances material inhomogenities material transitions Glass cylinder oven Glass profile temperature Heat temperature diameter thickness pulling speed S- Sensor A- Actuator Fraunhofer IOSB 2

Disturbances of the Process Diameter Startup stationär Cylinder

phase, end phase and cylinder transition additional radiation Pulling

3 Disturbances of the Process Diameter Startup stationär Cylinder transition End phase Wall Thickness Strong disturbances in Startup phase, end phase and cylinder transition additional radiation Pulling Speed Pressure Oven temperature (change of setpoint) Glass Temperature (changes of setpoint)... causes temperature disturbances Cylinder Temperature (changes of setpoint) Aim: model based temperature stabilization Fraunhofer IOSB 3

4 Equation for glass forming process Trouton Model (1D) Navier-Stokes equation systems 1 continuity Equation 3 momentum balance (3D) 1 Energy balance 1D Equation for glass-rod 3 log Temperature Profile of the Furnace 2 Tube decay constant abelow will be adapted Heating Tube decay constant aabove will be adapted Cylinder Fraunhofer IOSB 4

5 Local perturbation in Partial Differential Equation system S(r) Inhomogeous term Δ Given distributed system (IBVP) PDE,,, parameter Δ r BC IC, for Ω, Ω nominal solution, R(r) System response Δ,,, Δ Ω, Δ The change by local variation compare to nominal solution L r Fraunhofer IOSB 5

6 Numerical Sensitivity Analysis Sensitivity = Gâteaux variation Δ x ; lim Nominal Solution,, for perturbation Solution with perturbation, Calculate the term for variation of around Δ Find the limit ; lim Fraunhofer IOSB 6

7 Use of Comsol Multiphysics 1D Model 3 Multiphysics Mass balance Momentum balance Energy balance calculate,,,,, with parameter sweep for variation Fraunhofer IOSB 7

8 Disturbance analysis in Glass tube drawing process Spatial-description disturbance remains place fixed Material-description disturbance moves with material Δ, Δ Temperature Profile of the Furnace Tube decay constant a below will be adapted Heating Tube decay constant a above will be adapted Cylinder Q rad Q rad Collar Weld as radiation source Cylinder Fraunhofer IOSB 8

9 Stationary disturbance scenario fixed place disturbance Δ exp 1 2 Δ T oven T oven + T oven Fraunhofer IOSB

10 Sensitivity Index Δ/ Δ/ (T/T oven )(T oven /T).5 Sensitivity Index Glass Temperature -.5 (v/t oven )(T oven /v) 5 Sensitivity Index Velocity Max. sensitivity -5 (A/T oven )(T oven /A) 5 Sensitivity Cross Section Area T oven [K] -5 4 Max. sensitivity Disturbance Oven Temperature z [m] Fraunhofer IOSB 1

11 Transient disturbance scenario (Moving welding point).1 Geometric Profile (+- radius) , Q rad [W/m] Collar Q [kw/m] Heat Source of Disturbance height z [m]. Q rad Weld as radiation source Cylinder Fraunhofer IOSB 11

12 Simulation of moving welding point (snapshots) Fraunhofer IOSB 12

13 Conclusion and Future work Approach: Method to compute the Local sensitivity of system response with regarding to variation 2 scenarios of disturbance Stationary disturbance (spatial fixed) Improved process comprehension Transient disturbance (material fixed) Close to reality process behavior Future works: Process optimization -> Find optimal control strategies to minimize of the welding point effect Parameter estimation (Disturbance, Oven Profile) Fraunhofer IOSB 13

Finite Element Model of a complex Glass Forming Process as a Tool for Control Optimization

Excerpt from the Proceedings of the COMSOL Conference 29 Milan Finite Element Model of a complex Glass Forming Process as a Tool for Control Optimization Felix Sawo and Thomas Bernard Fraunhofer Institute