Thermodynamic performance analysis of a round tube fitted with gradient quadruple twisted tapes

Air-cooled heat exchangers employing twisted-tape passive inserts exist in many forms; however, designing tapes that are practical to manufacture while enhancing heat transfer without incurring excessive pressure drop remains challenging. This study therefore introduces gradient quadruple twisted tapes (GQTT), which gradually vary the pitch across four tapes to control swirl and mix along the tube. In addition, the turn count changes in steps along the four tapes, which triggers extra turbulence near each change and keeps the flow well mixed downstream. This simple and manufacturable pattern aims to boost heat transfer while keeping the added friction under control. Our objective is to evaluate whether GQTT can improve overall performance while keeping the pressure drop within a practical range, in comparison with a plain tube and a constant-turn tape. A realizable k-ε turbulence model, rigorously validated against benchmark data, was applied to eight GQTT variants and benchmarked against a plain tube and a constant-turn tape for Reynolds numbers (Re) between 5000 and 19,000. Spatial second-order schemes, grid-independence testing, and strict residual criteria ensured solution accuracy. Among the candidates, the descending-opposite-pitch configuration (Ds-OPSD) consistently delivered the highest performance. First-law analysis reveals a peak thermal performance factor (TPF) of 1.42 at Re = 5000, equating to a 42 % gain in overall thermo-hydraulic efficiency over the plain tube, with the Nusselt number (Nu) climbing from 57.5 to 100 across the examined Re window. Second-law metrics corroborate this superiority. At the same Re of peak TPF, the Ds-OPSD cuts exergy destruction from 291.4 to 62 W (≈79 % reduction versus the plain tube and ≈22 % versus the constant-turn tape). Total entropy generation remains minimal and nearly constant (Stotal ≈ 0.206–0.212), while the Bejan number stays high (≈0.999–0.971), indicating that the enhancement is achieved without excessive frictional penalties.