S V Karpushkin (Tambov State Technical University) :
Articles:
519.873 Modeling and optimization the process of liquid mechanical mixing in a vertical vessel
Karpushkin S. V. (Tambov State Technical University)
doi: 10.18698/2309-3684-2025-4-148172
A mathematical model of the mechanical mixing process (MMP) of a homogeneous liquid in a vertical capacitive apparatus is proposed, including the Reynolds-averaged Navier-Stokes equations and equations of semiempirical RNG k-ε model of turbulence in a cylindrical coordinate system. The conclusion about the adequacy of the proposed model is justified by comparing the mixing power consumption values, determined by calculations' results of the velocity field in stirred liquid and the results of laboratory and industrial experiments: measurements supply voltage for electric motor of a mechanical mixing device (MMD) and the current consumption when stirring a homogeneous liquid and rotating the stirrer in an empty apparatus. The problem's formulation of optimizing the MMD's parameters provides for the choice of values the diameter and height of the agitator blade, the height of its installation above the bottom of the apparatus and the rotation frequency of its shaft, minimizing the dispersion of the velocity vector's medium length of the mixed liquid. It is proposed to determine the values of MMD design's additional parameters by iteration at the optimal values of the above-mentioned basic parameters. The basis for the development of a numerical algorithm for solving the problem was the method of planning a multifactorial computational experiment. Examples of solving problems of optimizing design parameters and operating mode of MMDs of laboratory and industrial devices are given. The optimal blade widths of the most common mechanical agitators exceed those recommended by the NIIHIMMASH Guidance Document by 1.7-2.5 times. Based on the results of solving the problem of optimizing the MMD's parameters of the industrial apparatus of JSC Pigment, Tambov, modifications of its design were proposed, which made it possible to eliminate the formation of deposits on the walls of the apparatus, reduce by 10% the duration of the repulpation stage of the copper phthalocyanine paste, and reduce by 16% the cost of mixing power.
Карпушкин С.В. Моделирование и оптимизация процесса механического перемешивания жидкости в вертикальной емкости. Математическое моделирование и численные методы, 2025, № 4, с. 148–172.