Simulation of mixing process based on integrated multi-objective optimization and multi-criteria decision making

WU Yukun; LI Zhengquan; ZHANG Boqun; CHEN Huimin; WANG Yide; LI Kaixuan; LI Mingzhou

doi:10.13732/j.issn.1008-5548.2025.02.002

Abstract：Objective In optimizing the design of stirred tanks,the difficulty lies in the variability of structural parameters,operating condi-tions,and constraints among them.Enhancing performance in one aspect may sacrifice the efficiency of others,making it diffi-cult to achieve systematic optimization and increasing design costs.Striking a balance between maximizing stirring efficiency and minimizing energy consumption is a major challenge in the optimization of stirred tank operation.Based on the developed computational fluid dynamics-artificial neural network(CFD-ANN)data prediction model,a multi-criteria decision-making method that reflects different decision-makers'preferences is used to address the challenge in balancing energy consumption and stirring efficiency of stirred tanks in different industrial applications. Methods The CFD-ANN data prediction model was optimized using non-dominated sorting genetic algorithm Ⅱ(NSGA Ⅱ)to obtain the Pareto solution set.The target weight ratio was determined by analyzing the influence of each variable through the entropy weight method and subjective weighting.The corresponding optimal solution was selected from the Pareto solution set for different industrial application scenarios using multi-criteria decision making approach. Results and Discussion Compared with the Base case,the balanced optimal solution(Opt1)reduced energy consumption by 52.49％,increased fluid mixing by 1.35％,and improved suspension uniformity by 72.31％.Decision-makers significantly improved the performance of stirred tanks by adjusting subjective weights,thereby influencing the selection of optimization solu-tions.To ensure industrial standards in key stirred tank parameters,increasing impeller speed and reducing baffle width were recommended.An impeller diameter of 2T/3 with a height of H/4 from the bottom optimized energy-saving,an impeller diameter of T/2.13 with a height of H/6 enhanced uniform fluid mixing,and an impeller diameter of T/1.94 with a height between H/5-H/6 promoted uniform particle suspension.Among the preferred optimal solutions based on different industrial application sce-narios,when decision-makers prioritized energy saving,an excessively large subjective weight for power number Np(w=[0.700.15 0.15])had a severe impact on other goals.When the subjective weight of Np was 0.4,the proposed solution could reduce energy consumption by 86.5％on average,increasing fluid mixing by 27.8％and maintaining solid particle suspension unifor-mity within the required σ.When decision-makers preferred optimal fluid mixing,the proposed scheme reached an ideal Nq in the Pareto solution set,with a value of 0.234 76.It was worth noting that when the optimal fluid dispersion was preferred,a uni-form suspension of solid particles could also be achieved under the effect of fluids,yielding an excellent standard deviation of solid concentration of 0.087 11.Compared to the Base case,this scheme showed superiority in improving fluid dispersion char-acteristics within the tank and the upward transport capability for solid particles.When decision-makers preferred a more uni-form solid suspension,the proposed solution,though not outstanding in terms of optimizing energy consumption and fluid mix-ing,still achieved significant improvements of 54.45％and 33.49％in these two performance indicators compared to the Base case,with the standard deviation of solid concentration reduced to 9.93％of the Base case,showing relatively superior perfor-mance.It was worth noting that the Np under this preference did not reach the maximum value in the Pareto solution set,indicat-ing that the system performed well in balancing energy consumption and uniform mixing of solid particles. Conclusion The study,based on a multi-objective optimization model,investigates the impact of varying subjective weights on various dependent variables.It finely controls Np,Nq,and σ in stirred tanks based on different decision-making preferences to obtain optimal solutions that meet specific needs.The performance of each preferred optimal solution is evaluated.A new method is introduced to balance multiple conflicting objectives in stirred tank optimization,and corresponding optimal solutions are proposed based on different decisions.It provides theoretical support and reference for stirred tank performance optimization and industrial production.