Melt Spinning: Optimal Control and Stability Issues
Identifieur interne : 000591 ( Main/Exploration ); précédent : 000590; suivant : 000592Melt Spinning: Optimal Control and Stability Issues
Auteurs : Thomas Götz [Allemagne] ; Shyam S. N. Perera [Sri Lanka]Source :
English descriptors
- Teeft :
- Adjoint, Adjoint system, Adjoint variable, Algorithm, Arnoldi method, Boundary condition, Classical form, Coefficient, Control variable, Cost functional, Decent algorithm, Different weighting coefficient, Differentiable function, Dimensionless form, Eigenvalue, Eigenvalue problem, Extrusion speed, Extrusion velocity, Fiber formation process, Final temperature, Heat transfer coefficient, Implicit method, Industrial application, Industrial process, Inflow velocity, Initial profile, Initial value problem, Intermediate profile, Isothermal, Isothermal newtonian case, Iterative method, Linear regression, Linear stability analysis, Linearized equation, Linearized system, Many research group, Mass balance, Mathematical model, Minimization problem, Model figure, Momentum balance, Newtonian, Newtonian case, Newtonian model, Numerical computation, Numerical result, Numerical solution, Numerical value, Optimal control, Optimality condition, Optimality system, Optimization, Optimization problem, Optimization question, Optimized profile, Parameter value, Perera, Polymer, Polymer fiber, Polymeric material, Process condition, Process parameter, Process stability, Resonance instability, Rice university, Sect, Shooting method, Single filament, Small perturbation, Solid line, Spinline, Spinline velocity, Stability analysis, Stability domain, Stability issue, State system, State variable, Steepest descent algorithm, Step size, Stiff differential equation, Table critical, Temperature profile, Viscous polymer, Weighting, Weighting coefficient.
Abstract
Abstract: A mathematical model describing the melt spinning process of polymer fibers is considered. Newtonian and non-Newtonian models are used to describe the rheology of the polymeric material. Two key questions related to the industrial application of melt spinning are considered: the optimization and the stability of the process. Concerning the optimization question, the extrusion velocity of the polymer at the spinneret as well as the velocity and temperature of the quench air serve as control variables. A constrained optimization problem is derived and the first-order optimality system is set up to obtain the adjoint equations. Numerical solutions are carried out using a steepest descent algorithm. Concerning the stability with respect to variations of the velocity and temperature of the quench air, a linear stability analysis is carried out. The critical draw ratio, indicating the onset of instabilities, is computed numerically solving the eigenvalue problem for the linearized equations.
Url:
DOI: 10.1007/978-90-481-9981-5_5
Affiliations:
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N." last="Perera">Shyam S. N. Perera</name><affiliation wicri:level="1"><country xml:lang="fr">Sri Lanka</country><wicri:regionArea>Department of Mathematics, University of Colombo, Colombo 03</wicri:regionArea><wicri:noRegion>Colombo 03</wicri:noRegion></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Sri Lanka</country></affiliation></author></analytic><monogr></monogr></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="Teeft" xml:lang="en"><term>Adjoint</term><term>Adjoint system</term><term>Adjoint variable</term><term>Algorithm</term><term>Arnoldi method</term><term>Boundary condition</term><term>Classical form</term><term>Coefficient</term><term>Control variable</term><term>Cost functional</term><term>Decent algorithm</term><term>Different weighting coefficient</term><term>Differentiable function</term><term>Dimensionless form</term><term>Eigenvalue</term><term>Eigenvalue problem</term><term>Extrusion speed</term><term>Extrusion velocity</term><term>Fiber formation process</term><term>Final temperature</term><term>Heat transfer coefficient</term><term>Implicit method</term><term>Industrial application</term><term>Industrial process</term><term>Inflow velocity</term><term>Initial profile</term><term>Initial value problem</term><term>Intermediate profile</term><term>Isothermal</term><term>Isothermal newtonian case</term><term>Iterative method</term><term>Linear regression</term><term>Linear stability analysis</term><term>Linearized equation</term><term>Linearized system</term><term>Many research group</term><term>Mass balance</term><term>Mathematical model</term><term>Minimization problem</term><term>Model figure</term><term>Momentum balance</term><term>Newtonian</term><term>Newtonian case</term><term>Newtonian model</term><term>Numerical computation</term><term>Numerical result</term><term>Numerical solution</term><term>Numerical value</term><term>Optimal control</term><term>Optimality condition</term><term>Optimality system</term><term>Optimization</term><term>Optimization problem</term><term>Optimization question</term><term>Optimized profile</term><term>Parameter value</term><term>Perera</term><term>Polymer</term><term>Polymer fiber</term><term>Polymeric material</term><term>Process condition</term><term>Process parameter</term><term>Process stability</term><term>Resonance instability</term><term>Rice university</term><term>Sect</term><term>Shooting method</term><term>Single filament</term><term>Small perturbation</term><term>Solid line</term><term>Spinline</term><term>Spinline velocity</term><term>Stability analysis</term><term>Stability domain</term><term>Stability issue</term><term>State system</term><term>State variable</term><term>Steepest descent algorithm</term><term>Step size</term><term>Stiff differential equation</term><term>Table critical</term><term>Temperature profile</term><term>Viscous polymer</term><term>Weighting</term><term>Weighting coefficient</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: A mathematical model describing the melt spinning process of polymer fibers is considered. Newtonian and non-Newtonian models are used to describe the rheology of the polymeric material. Two key questions related to the industrial application of melt spinning are considered: the optimization and the stability of the process. Concerning the optimization question, the extrusion velocity of the polymer at the spinneret as well as the velocity and temperature of the quench air serve as control variables. A constrained optimization problem is derived and the first-order optimality system is set up to obtain the adjoint equations. Numerical solutions are carried out using a steepest descent algorithm. Concerning the stability with respect to variations of the velocity and temperature of the quench air, a linear stability analysis is carried out. The critical draw ratio, indicating the onset of instabilities, is computed numerically solving the eigenvalue problem for the linearized equations.</div></front></TEI><affiliations><list><country><li>Allemagne</li><li>Sri Lanka</li></country><region><li>Rhénanie-Palatinat</li></region><settlement><li>Kaiserslautern</li></settlement></list><tree><country name="Allemagne"><region name="Rhénanie-Palatinat"><name sortKey="Gotz, Thomas" sort="Gotz, Thomas" uniqKey="Gotz T" first="Thomas" last="Götz">Thomas Götz</name></region><name sortKey="Gotz, Thomas" sort="Gotz, Thomas" uniqKey="Gotz T" first="Thomas" last="Götz">Thomas Götz</name></country><country name="Sri Lanka"><noRegion><name sortKey="Perera, Shyam S N" sort="Perera, Shyam S N" uniqKey="Perera S" first="Shyam S. N." last="Perera">Shyam S. N. Perera</name></noRegion><name sortKey="Perera, Shyam S N" sort="Perera, Shyam S N" uniqKey="Perera S" first="Shyam S. N." last="Perera">Shyam S. N. 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