The development of power-law preconditioning approach for simulation of unsteady viscoelastic flows

Document Type : Research Article

Authors

1 Energy Conversion, Faculty of Mechanics, Shahroud University of Technology, Shahroud

2 Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

3 Faculty of Mechanical Engineering, Shahrood University of Technology

Abstract

One of the particular features of viscoelastic liquids in unstable shear flows is the damping oscillatory behavior in the velocity field without imposing external force and oscillation. This behavior is seen because of the elastic property of the liquid. In the present paper, for the first time, the preconditioning method of local stress censor has been employed for numerically simulating unstable viscoelastic liquids passing through fixed parallel plates. In this regard, the Maxwell model has been used. In this method, by adding fake time derivation to governing equation, hyperbolic equations will be generated. By obtaining the preconditioning matrix of these equations corrected locally through the power relation of stress field and employing binary algorithm for time including inner and outer loop, solving incompressible unsteady flows can be possible in the form of artificial compressible flows. In order to converge the inner loop, the four-step Vossooghifar's method has been implemented. Equations were discretized through the finite difference and shifted network. Calculation of unsteady viscoelastic flows has been performed for various Reynolds numbers, Weissenberg numbers and viscosity ratios have been presented. The results are in good agreement with the numerical results. Results of the convergence rate indicate that the locally preconditioning power censor method is the appropriate one for a viscosity ratio lower than 0.5 demonstrating a higher convergence rate and reduced time cost of calculations.

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References

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Amirkabir Journal of Mechanical Engineering
Volume 55, Issue 3
June 2023
Pages 381-406

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