Carreau’s Rheological Model and A.N. Tikhonov’s Regularization Method: Parametric Identification Based on a CFD model

Abstract

Introduction. Carreau's rheological model can describe the three-dimensional flows of non-Newtonian media. However, it requires modeling parameters for the viscosity of the medium at the limiting values of shear rates, which cannot be achieved by instrumental methods. The present article introduces a novel method that can identify the parameters of Carreau’s model using a regularization algorithm. Study objects and methods. The study featured fondant mass produced according to the traditional formulation for Creamy Fondant unglazed candies. Standard methods were used to describe the properties of the raw materials and semi-finished products, as well as methods of mathematical processing, modeling, and optimization. Results and its discussion. The research produced an algorithm based on A.N. Tikhonov’s regularization method of the parametric identification of Carreau's rheological model. The calculation residual was minimized by the viscometric measurements and the CFD model, which provided the calculation of the hydrodynamic flow regime at the limiting values of shear rates. The CFD model of a steady non-isothermal flow of a nonlinear viscous medium through a cylindrical capillary was based on the equations of conservation of mass, energy, and momentum. The rheological parameters of Carreau’s model were illustrated by the case of fondant mass. The error for the viscosity prediction did not exceed 14.07%. Conclusion. The parametric identification algorithm made it possible to evaluate the rheological parameters of structured liquid media with Carreau's rheological law in cases that lack experimental information on the behavior of the medium at limiting shear rates. The algorithm eliminated the computational problems typical of Ostwald and de Ville’s rheological model, which usually arise when solving practical problems of three-dimensional flows of non-Newtonian media with limiting viscosity values.

Keywords

• regularization
• identification
• rheological model
• carreau fluid model
• hydrodynamics
• cfd-model