Abstract
The most widely adopted constitutive model of viscoelastic flows based on the kinetic theory is the FENE (Finitely Extensible Nonlinear Elastic) model. This model represents a polymer molecule by a dumbbell which consists of two beads connected by a spring. The direction and elongation of the spring are described by the Fokker–Planck equation. The two important parameters in the Fokker–Planck equation, which represent the relaxation time and the maximum extensibility of the dumbbell, determine the viscoelasticity of flows and affect the velocity fields. In the present work, we devise a method of estimating these two parameters using velocity measurements. The relevant inverse problem is solved by converting it to a minimization problem of a performance function employing a conjugate gradient method. The present scheme is shown to estimate these structural parameters even with noisy velocity measurements.
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