Multi-objective optimization of liquid-liquid mixing in helical pipes using Genetic Algorithms coupled with Computational Fluid Dynamics

The identification of the best possible helical pipe geometry for optimal mixing is challenging since the two central objectives (minimizing pressure drop while maximizing mixing efficiency) cannot be reached simultaneously; they lead to concurrent target functions. The present study identifies optimal configurations using multi-objective optimization for the flow of two miscible liquids in helical pipes. A flow optimization library (OPAL++) was used to automatically control the numerical simulations. The objective is to optimize the helical pipe dimensions, maximizing mixing efficiency (M-c) and simultaneously minimizing the pressure drop per unit length (Delta P/L). The pipe diameter (d), coil diameter (D) and pitch (P), were widely varied within 4-50 mm, 10-500 mm, and 5-100 mm, respectively. Additionally, the Reynolds number (Re) was varied within 20-60, covering the optimal range for liquid mixing in helical pipes. After performing a total of 1226 simulations over 30 optimization generations, a Pareto front was obtained, containing all concurrent optimal solutions. The results revealed that the reduction of any of the geometrical parameters can generally improve mixing. The change of D or P slightly affects the pressure drop, while the reduction of d increases the pressure drop significantly. All configurations in the Pareto front show a strong linear correlation between d and P, showing that P should be kept as small as possible. A globally optimal individual is suggested based on minimizing the Euclidean distance to the extreme point of the objective functions (M-c = 1, Delta P/L = 0). Finally, correlations are proposed for predicting the pressure drop and the mixing coefficient. The resulting optimal geometry and its associated process conditions are recommended to ensure excellent mixing at minimum pumping power.