Thermal Performance of an Air Channel with Cylindrical Cross-bars

Abstract

Heat exchangers are used in a wide variety of industrial applications. Augmentation of heat transfer can realize a reduction in heat transfer size and increase the effectiveness and efficiency of heat exchangers. Heat transfer can be enhanced with various methods where the turbulence of the fluid flow is enhanced: by adding ribs, grooves or steps to the channel wall, using helical inserts, or by adding bluff bodies in the channel flow. By using these methods, there is also an increase in pressure drop penalty and larger pumping power is required to achieve the same flow rate. Circular cylindrical bluff bodies have been found to have smaller drag coefficients than square, rectangular or triangular cylindrical bluff bodies in the channel flow. Heat transfer and pressure drop experimental tests were done for eight different circular cylindrical cross-bar arrays at 15 different Reynolds numbers, in the range of 640 to 12 500. Eight different cross-bar configurations were tested: the cylinder diameter to pitch ratios were, d/p = 0.025, d/p = 0.05, d/pi=i0.1 and d/p = 0.2, and the angle to the flow direction, was θ = 90° and θ = 45° for each of the four different diameter-to-pitch ratios. Transient CFD simulations were done using Ansys fluent for d/p = 0.05 and d/p = 0.2, for θ = 90°, at Reynolds numbers 920 and 9 700, to analyze the secondary flow structures in the wake of the cylinders, partly responsible for the heat transfer and pressure drop increase in the channel flow in comparison to the smooth channel. The k-Ω shear stress transport (SST) model was used for the simulations. A mesh dependence study was done for spatial discretization, temporal discretization and validated against the experimental setup. The pressure drop gradient was found from the test data for the hydraulically developed part of the test section to calculate the friction factors. With an increase in Reynolds number, the friction factors decreased until reaching an asymptotic value for all the cross-bar configurations. For θi=i90° the friction factors were larger than for θ = 45° for the same d/p ratio and Reynolds number. With an increase in d/p, the friction factors increased. The largest measured friction factor was f = 0.3, for configuration d/p = 0.2, θ = 90°, at Re = 640 and the smallest measured friction factor f = 0.02, for d/pi= 0.025, θ = 45°, at Re = 12 500. The friction factor ratio was then used to quantify the pressure penalty for using cylindrical cross-bars in the channel flow to enhance heat transfer. The maximum friction factor ratio, f/f0 = 16.7 occurred at Re = 9 700, for d/pi=i0.2, θ = 90° and the minimum friction factor ratio, f/f0 = 2.1, at Re = 640, for d/pi=i0.025, θ = 45°. The average Nusselt numbers were then calculated using the spatial integral average of the local Nusselt numbers. With an increase in Reynolds number, there was an increase in the average Nusselt number for all the cylindrical cross-bar configurations. For larger d/p ratios and θ = 90° cases, the average Nusselt numbers were larger than for smaller d/p ratios and θ = 45°. The largest average Nusselt number was Nuavg = 66.3, at Re = 9 700 for d/p = 0.2, θ = 90° and the smallest average Nusselt number, Nuavg = 8.7, at Re = 640 for d/p = 0.025, θ = 45°. The Nusselt number ratio could then be used to quantify the heat transfer enhancement of the cylindrical cross-bar channel to that of the smooth channel, where the largest Nusselt number ratio was, Nuavg /Nu0,avg = 3.3, for d/p = 0.2, θ = 90°, at Rei=i3 000 and the smallest Nuavg /Nu0,avg = 1.1, for d/p = 0.025, θ = 45°, at Re = 640. The CFD results concluded that the pressure drop increase and heat transfer enhancement were caused by the flow acceleration, flow separation, eddy formation, vorticity increase, and boundary layer deformation next to and behind the cylinders. The Strouhal number for the larger d/p ratios suggested that the unsteadiness in the flow is higher for the cylinder arrays with a larger diameter, increasing both the heat transfer enhancement and friction factor in comparison with the smaller diameter cylinder arrays. Finally, the thermal performance coefficients could be calculated by using the friction factor ratios and Nusselt number ratios. The thermal performance coefficient combines the effects of the heat transfer and pressure penalty increase. The thermal performance coefficients increased from Re = 640 until Rei=i3 000 after which it decreased with an increase in Reynolds number. This is because the pressure penalty starts to outweigh the heat transfer increase caused by the turbulators. The largest thermal performance coefficient was η = 1.6, for d/p = 0.025, θ = 45°, at Re = 3 000, and the lowest, η = 0.79, for d/p = 0.05, θ = 90°, at Re = 640.