Development and validation of Nusselt number correlations for a helical coil based energy storage integrated with solar water heating system

Abstract

Storage tanks based on helical coil heat exchangers are an integral part of solar water heating systems and require optimal design configuration to achieve maximum heat transfer and a longer storage period. This study is focused on thermal analysis of a vertical helical coil-based water storage tank and derivation of inner and outer Nusselt number correlations by considering the storage tank as well as helical coil and catering to both forced and natural convection effects. A fluid-fluid conjugate heat transfer transient state model is validated with experiments performed with 50/50 % water-glycol mixture as heat transfer fluid at flow rates of 2 and 3 L/min in a solar water heating system, while water remains at static flow condition inside the tank. To reduce the computational cost, a symmetrical downsized (50 % of the real storage tank size) model is also designed and validated, which showed a mean absolute percentage error of 3.25 %. In order to derive the mathematical correlations, alterations were made to the validated model by using coils with curvature ratios ranging from 0.09 to 0.184 with HTF flow rates in laminar flow regimes, ranging from 30 to 100 L h−1 at temperatures from 40 °C to 80 °C. Furthermore, inner Nusselt number mathematical correlations based on M number, curvature ratio, and Prandtl number showed good agreement with correlations derived by past investigators. Similarly, the outer Nusselt number of the coil was related to Rayleigh's number and the derived relations showed good agreement with the past studies, while Nuo = 0.1996 (Rado0.326) showed the least error of 2.06 %. Finally, thermal stratification analysis helped to understand that coil position and aspect ratio determine the thermocline developed inside the storage tank. Results show that extension of coil inside the tank up to 83.7 % of the tank height, ensured greater thermocline range, and tank with aspect ratio 3 turned to be better for thermal energy storage for longer period.