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Glass 1 Radiative Heat transfer and Applications for Glass Production Processes Axel Klar and Norbert Siedow Department of Mathematics, TU Kaiserslautern.

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Presentation on theme: "Glass 1 Radiative Heat transfer and Applications for Glass Production Processes Axel Klar and Norbert Siedow Department of Mathematics, TU Kaiserslautern."— Presentation transcript:

1 Glass 1 Radiative Heat transfer and Applications for Glass Production Processes Axel Klar and Norbert Siedow Department of Mathematics, TU Kaiserslautern Fraunhofer ITWM Abteilung Transport processes Montecatini, 15. – 19. October 2008

2 Glass 2 Radiative Heat transfer and Applications for Glass Production Processes Planning of the Lectures 1.Models for fast radiative heat transfer simulation 2.Indirect Temperature Measurement of Hot Glasses 3.Parameter Identification Problems

3 Glass 3 Parameter Identification Problems N. Siedow Fraunhofer-Institute for Industrial Mathematics, Kaiserslautern, Germany Montecatini, 15. – 19. October 2008

4 Glass 4 Parameter Identification Problems Outline 1.Introduction 2.Some Basics 3.Shape Optimization of Pipe Flanges 4.Impedance Tomography 5.Further Examples 6.Optimization of Thermal Stresses 7.Conclusions

5 Glass 5 Example 2:Parameter Identification Conductivity is unknown Additional information: Measurement Formally we can writeor We have to calculate derivatives! Parameter Identification Problems 1. Some Basics

6 Glass 6 A very convenient way of calculating derivatives is the Adjoint Method subject to (Partial Differential Equation) Lagrangian: Derivatives: State Equation Adjoint Equation Parameter Equation Parameter Identification Problems 1. Some Basics

7 Glass 7 Example 2: subject to (Partial Differential Equation) Lagrangian: Derivatives: State Equation Adjoint Equation Parameter Equation + b. c. Parameter Identification Problems 1. Some Basics

8 Glass 8 Example 2: subject to (Partial Differential Equation) Parameter Identification Problems 1. Some Basics

9 Glass 9 Example 2: subject to(Partial Differential Equation) Parameter Identification Problems 1. Some Basics

10 Glass 10 Electric heating to keep the glass at desired temperature Control temperature (e.g. to avoid solidification) Control the input current (hot spots, cold shocks) Shape Optimization Constraints: Objective: Parameter Identification Problems 2. Shape Optimization of Pipe Flanges

11 Glass 11 Find a surface shape of the flange so, that in a small section near the pipe boundary: Under certain constraints: Equation of electrical potential (1) Heat transfer equation (2)... Parameter Identification Problems 2. Shape Optimization of Pipe Flanges

12 Glass 12 (2) (1) Parameter Identification Problems 2. Shape Optimization of Pipe Flanges 3D Model

13 Glass 13 Flange is very thin compared to the other dimensions Assume: the shape of the flange is symmetric with respect to z electrical potential: - small parameter Parameter Identification Problems 2. Shape Optimization of Pipe Flanges Asymptotic Approach

14 Glass 14 Electrical potential: + boundary conditions Heat transfer: (3) (4) Parameter Identification Problems 2. Shape Optimization of Pipe Flanges Asymptotic Approach

15 Glass 15 Find of the flange so, that in near the pipe Under certain constraints: Equation of electrical potential (3) Heat transfer equation (4)... Minimal material Parameter Identification Problems 2. Shape Optimization of Pipe Flanges Parameter Optimization

16 Glass 16 Lagrangian method: Potential equation (3) Heat transfer equation (4) Total Lagrangian Necessity condition Adjoint potential equation Adjoint heat transfer equation Parameter Identification Problems 2. Shape Optimization of Pipe Flanges

17 Glass 17 Before optimizationAfter optimization Thickness Parameter Identification Problems 2. Shape Optimization of Pipe Flanges Example

18 Glass 18 Before optimizationAfter optimization Temperature Parameter Identification Problems 2. Shape Optimization of Pipe Flanges Example

19 Glass 19 Before optimizationAfter optimization Heat Flux Parameter Identification Problems 2. Shape Optimization of Pipe Flanges Example

20 Glass 20 The knowledge of the temperature of the glass melt is important to control the homogeneity of the glass Glass melting in a glass tank Parameter Identification Problems 3. Impedance Tomography

21 Glass 21 Thermocouples at the bottom and the sides of the furnace Use of pyrometers is limited due to the atmosphere above the glass melt Parameter Identification Problems 3. Impedance Tomography

22 Glass 22 Glass melt Determine the temperature of the glass melt during the melting process apply Electric current measure Voltage Neutral wire Experiment electrode Parameter Identification Problems 3. Impedance Tomography

23 Glass 23 Parameter Identification Problems 3. Impedance Tomography The forward Problem

24 Glass 24 Parameter Identification Problems 3. Impedance Tomography The forward Problem Electric potential Electric current density

25 Glass 25 Parameter Identification Problems 3. Impedance Tomography The inverse Problem Findso that under the constraints that 2.is solution of the (so-called) form equation 1.is solution of the potential equation Looking for a smooth solution

26 Glass 26 Parameter Identification Problems 3. Impedance Tomography The inverse Problem Potential Equation Adjoint Potential Equation Adjoint Form Equation New Form Function

27 Glass 27 Example originalReconstruction Parameter Identification Problems 3. Impedance Tomography

28 Glass 28  Heat Transfer Coefficient Dip Experiment Parameter Identification Problems 4. Further Examples

29 Glass 29  Brinkmann, Siedow. „Heat Transfer between Glass and Mold During Hot Forming.“ In Krause, Loch: Mathematical Simulation in Glass Technology; Springer 2002  Heat Transfer Coefficient Parameter Identification Problems 4. Further Examples

30 Glass 30  Initial condition  Boundary condition Control Problem Parameter Identification Problems 4. Further Examples

31 Glass 31 Wrong cooling of glass and glass products causes large thermal stresses Undesired crack Parameter Identification Problems 6. Optimization of Thermal Stresses

32 Glass 32  Thermal tempering consists of:  Heating of the glass at a temperature higher the transition temperature  Very rapid cooling by an air jet Better mechanical and thermal strengthening to the glass by way of the residual stresses generated along the thickness  N. Siedow, D. Lochegnies, T. Grosan, E. Romero, J. Am. Ceram. Soc., 88 [8] 2181-2187 (2005) Parameter Identification Problems 6. Optimization of Thermal Stresses

33 Glass 33 How to control the heating to achieve a predefined temperature profile inside the glass products? Parameter Identification Problems 6. Optimization of Thermal Stresses

34 Glass 34 Linear CoolingOptimized Cooling Minimize thermal stresses during the cooling process Parameter Identification Problems 6. Optimization of Thermal Stresses

35 Glass 35 Used CoolingThermal Stress Minimize the cooling time with constraint that permanent thermal stress < 3.5 Mpa Parameter Identification Problems 6. Optimization of Thermal Stresses

36 Glass 36 -24% 691s 915s Used CoolingThermal Stress Minimize the cooling time with constraint that permanent thermal stress < 3.5 Mpa Parameter Identification Problems 6. Optimization of Thermal Stresses

37 Glass 37 Optimal Mould Design during Pressing How to design the mould that after cooling the glass lens has the desired shape?  Sellier, Breitbach, Loch, Siedow.“An iterative algorithm for optimal mould design in high-precision compression moulding.“ JEM606, IMechE Vol.221,2007, 25-33 Parameter Identification Problems 6. Optimization of Thermal Stresses

38 Glass 38 Deviation of the upper glass side from the desired shape Parameter Identification Problems 6. Optimization of Thermal Stresses Deviation of the lower glass side from the desired shape

39 Glass 39  Parameter Identification Problems are inverse problems Ill-posedRegularization  We have discussed different Parameter Identification Problems  For constraint optimization problems the Lagrangian approach is very convenient for calculating derivatives Parameter Identification Problems 7. Conclusions

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