Field synergy analysis for helical ducts with rectangular cross section

This paper proposes a new approach based on VSP method (Vorticity-Stream function-Poisson equation method), to study numerically fully developed laminar flow characteristics and heat transfer behaviors of helical ducts with rectangular cross section. The aim is to guide heat transfer enhancement for helical rectangular ducts. Based on the numerical results, synergies between velocity field and temperature field have been investigated through field synergy principle. The effects of curvature, torsion, aspect ratio, Reynolds number, and Prandlt number on velocity field, temperature field and field synergy have been examined. The results show that the secondary flow of the central regions is weaker than that in other locations of the cross section. With reference to the entire cross section, the best values of synergy between velocity field and temperature field can be found in the center of the section. Increasing the curvature, Reynolds number and Prandtl number causes the mean synergy angles of the cross section to increase. This result indicates that it is more important to improve the field synergy for high Prandlt number fluid, especially at high Reynolds number. As the torsion increases, the average synergy angles decreases. The mean synergy angles reach the maximum value when the aspect ratio is equal to one; therefore, one can conclude that the field synergy of helical ducts with square cross section is the worst. To enhance heat transfer performance of helical rectangular ducts, for small aspect ratio, the main important aspect is to improve the secondary flow in the center of the cross section. On the contrary, for moderate values of the aspect ratio, the most important aspect is to improve the field synergy of the region near the upper and the lower wall. The correlations of friction factor and Nusselt number have been also developed for helical ducts with rectangular cross section.