Observability of viscoelastic fluids
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Authors
Zhou, Hong
Kang, Wei
Krener, Arthur
Wang, Hongyun
Subjects
Observability
Observability rank condition
Unscented Kalman filter
Viscoelastic models
Observability rank condition
Unscented Kalman filter
Viscoelastic models
Advisors
Date of Issue
2010
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Abstract
We apply the observability rank condition to study the observability of various viscoelastic fluids under imposed shear or extensional flows. In this paper the observability means the ability of determining the
viscoelastic stress from the time history of the observations of the first normal stress difference. We consider four viscoelastic models: the upper convected Maxwell (UCM) model, the PhanﾖThienﾖTanner
(PTT) model, the JohnsonﾖSegalman (JS) model and the Giesekus model. Our study reveals that all of the four models have observability for all stress components almost everywhere under shear flow whereas
under extensional flow most of the models have no observability for the shear stress component. More specifically, for UCM and JS models under imposed shear flow, the observations of the first normal stress
difference allow the reconstruction of all components of viscoelastic stress. For UCM and JS models under extensional flow, the two normal stress components can be determined from the measurements of the
first normal stress difference; the shear stress component does not affect the evolution of the normal stress components and consequently it cannot be extracted from the observations. Under shear flow,
the PTT and Giesekus models have observability almost everywhere. That is, all components of the viscoelastic stress can be determined from the observations when the vector formed by the components of
viscoelastic stress does not lie on a certain surface. Under extensional flow, the PTT model has observability almost everywhere for normal stress components whereas the Giesekus model has observability
almost everywhere for all stress components. We also run simulations using the unscented Kalman filter (UKF) to reconstruct the viscoelastic stress from observations without and with noises. The UKF yields
accurate and robust estimates for the viscoelastic stress both in the absence and in the presence of observation noises.
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Article
Description
The article of record as published may be located at http://dx.doi.org/10.1016/j.jnnfm.2010.01.025
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Applied Mathematics
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Citation
Journal of Non-Newtonian Fluid Mechanics / Volume 165, 425-434
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.