MECHANICS

Mathematical modeling of power-law fluid flow in a mixer with a blade stirrer

E. I. Borzenko, D. N. Garbuzov, M. A. Efremov

Tomsk State University, pr. Lenina, 36, Tomsk, 634050, Russia

Abstract: The article presents the results of mathematical modeling of a power-law fluid flow in a blade stirrer mixing apparatus. The numerical solution of the problem is based on the control volume method and the SIMPLE procedure implemented on a non-uniform orthogonal grid. The distribution pattern of kinematic characteristics in the volume is investigated, and the flow structure is studied with the allocation of characteristic circulation zones for pseudoplastic, Newtonian and dilatant rheologies. To assess the mixing process over time, the problem of redistribution of an ensemble of marker particles initially located in the selected region and moving with the velocity of the medium is solved. Parametric studies of two technological criteria are carried out: the integral of the dissipative function showing the energy costs of organizing the flow; the original characteristic calculated from the current distribution of marker particles, allowing one to estimate the homogeneity of mixing.

Keywords: mixing apparatus, blade, power-law fluid, mathematical modeling, flow structure, circulation zone, mixing quality

UDC: 532.517.2, 66.063.8

MSC: 76A05, 76M12

Received: 15.05.2025
Accepted: 10.07.2025

DOI: 10.35634/vm250307

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