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On numerical simulation of liquid polymer moulding

    R. Čiegis Affiliation
    ; O. Iliev Affiliation

Abstract

In this paper we consider numerical algorithms for solving the system of nonlinear PDEs, arising in modeling of liquid polymer injection. We investigate the particular case when a porous preform is located within the mould, so that the liquid polymer is flowing through a porous medium during the filling stage. The nonlinearity of the governing system of PDEs is due to the non‐Newtonian behavior of the polymer, as well as due to the moving free boundary. The last is related to the penetration front, and a Stefan type problem is formulated to account for it. A finite‐volume method is used to approximate the given differential problem. Results from numerical experiments are presented.


We also solve an inverse problem and present algorithms for determination of the absolute preform permeability coefficient for the case when the velocity of the penetration front is known from the measurements.


In both considered cases (direct and inverse problems) we emphasize on the specifics related to the non‐Newtonian behavior of the polymer. For completeness, we discuss also the Newtonian case. Results of some experimental measurements are presented and discussed.


Polimerų filtracijos uždavinio skaitinis sprendimo algoritmas


Santrauka


Šiame darbe nagrinejamas skystu polimeru filtracijos uždavinio skaitinis sprendimo algoritmas. Matematinis modelis yra aprašomas netiesiniu diferencialiniu lygčiu dalinemis išvestinemis sistema. Del deformaciju filtracijos metu keičiasi uždavinio apibrežimo srities geometrija, be to skysčio filtracijos frontas irgi juda, todel formuluojamos dvi Stefano tipo kraštines salygos. Diskrečioji aproksimacija gaunama baigtiniu tūriu metodu.


Taip pat darbe sprendžiamas atvirkštinis mežiagos laidumo koeficiento nustatymo uždavinys. Gautos išreikštines formules Niutoninio ir apibendrinto Niutoninio skysčiu tekejimams. Šie teoriniai rezultatai palyginti su eksperimentiniais matavimu rezultatais.


First Published Online: 14 Oct 2010

Keyword : mathematical modeling, polymer moulding, finite‐volume method

How to Cite
Čiegis, R., & Iliev, O. (2003). On numerical simulation of liquid polymer moulding. Mathematical Modelling and Analysis, 8(3), 181-202. https://doi.org/10.3846/13926292.2003.9637223
Published in Issue
Sep 30, 2003
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