Heat Transfer Enhancement Using Spring and Twisted-Tape Turbulators: Performance, Entropy Generation, and Multi-Criteria Optimization

This study investigates the thermodynamic and hydraulic performance of spring and twisted-tape turbulators used to enhance heat transfer in turbulent pipe flow. Various geometries of spring and twisted-tape inserts were evaluated based on friction factor, Nusselt number, and total entropy generation. Additionally, total entropy generation number and Bejan number were used to assess the second-law efficiency. The results showed that entropy generation generally decreased with increasing Reynolds number for all configurations. The 43 and 63 mm spring inserts demonstrated superior thermodynamic performance, producing the lowest entropy and highest Bejan number values. In contrast, shorter twisted tapes, especially the 115 mm variant, caused higher frictional losses and irreversibility. Multi-objective optimization was conducted using Pareto front analysis and the technique for order preference by similarity to ideal solution (TOPSIS) method with five weighting strategies (Shannon entropy, equal weighting, CRiteria Importance Through Intercriteria Correlation, Analytic Hierarchy Process, and MEthod based on the REmoval Effects of Criteria). The 43 mm spring consistently ranked highest across all TOPSIS scenarios and dominated the Pareto front for Nu_f and Nu-S_{gen, total} spaces. In conclusion, the 43 mm spring insert provides the best balance between heat transfer and thermodynamic efficiency, making it the most effective solution among tested configurations. The study confirms that spring turbulators, particularly 43 and 63 mm variants, outperform twisted-tape designs in terms of second-law optimization and are recommended for energy-efficient heat exchanger applications.