Optimally staggered finned circular and elliptic tubes in forced convection

This work presents a numerical and experimental geometric optimization study to maximize the total heat transfer rate between a bundle of finned or non-finned tubes in a given volume and a given external flow both for circular and elliptic arrangements, for general staggered configurations. The optimization procedure started by recognizing the design limited space availability as a fixed volume constraint. The experimental results were obtained for circular and elliptic configurations with a fixed number of tubes (12), starting with an equilateral triangle configuration, which fitted uniformly into the fixed volume with a resulting maximum dimensionless tube-to-tube spacing S/2b=1.5, where S is the actual spacing and b is the smaller ellipse semi-axis. Several experimental configurations were built by reducing the tube-to-tube spacings, identifying the optimal spacing for maximum heat transfer. Similarly, it was possible to investigate the existence of optima with respect to other two geometric degrees of freedom, i.e., tube eccentricity and fin-to-fin spacing. The results are reported for air as the external fluid, in the range 852⩽Re L⩽8520, where L is the swept length of the fixed volume. Circular and elliptic arrangements with the same flow obstruction cross-sectional area were compared on the basis of maximum total heat transfer. This criterion allows one to quantify the heat transfer gain in the most isolated way possible, by studying arrangements with equivalent total pressure drops independently of the tube cross-section shape. The first part of the paper reports two-dimensional numerical optimization results for non-finned circular and elliptic tubes arrangements, which are validated by direct comparison with experimental measurements with good agreement. The second part of the paper presents experimental optimization results for non-finned and finned circular and elliptic tubes arrangements. A relative heat transfer gain of up to 20% is observed in the optimal elliptic arrangement, as compared to the optimal circular one. Both local optimal eccentricity (S/2b=0.25 and fixed fin-to-fin spacing) and local optimal fin-to-fin spacing (circular tube and S/2b=0.5) are shown to exist. Such findings motivate the search for global optima with respect to tube-to-tube spacing, eccentricity and fin-to-fin spacing in future three-dimensional numerical optimization studies.