Shape optimization of corrugated tube using B-spline curve for convective heat transfer enhancement based on machine learning

A significant way to achieve energy saving and emission reduction is to optimize the design of heat transfer devices. As is widely applied in industry, a corrugated tube constructed by B-spline curve is numerically investigated and the profile is optimized, using a surrogate model with considerations of performance evaluation criterion (PEC) as single objective or minimum flow resistance (f) and maximum Nusselt number (Nu) as multi-objective. The machine learning technique is used to determine the candidate samples to update the surrogate model for improving the optimization efficiency and reliability, which is validated to be effective in this paper The optimization results show that the comprehensive performance of the corrugated tube is more sensitive to the vertical coordinates of the control points, with the appropriate increase in the number of control points for B-spline, and the better performance of corrugated tubes is achieved The optimal profile corresponding to the best comprehensive performance is a double-crest shape. With Reynolds number (Re) increased, the wave-amplitude of the first wave gradually gets smaller, and the profile of the corrugated tube becomes smoother. With the increasing consideration of heat transfer performance over multi-objective optimization, the optimal shape gradually changes from a double-trough to a single-trough shape. Finally, the maximum PEC of 1.2415, 1.1845, and 1.1504 are acquired with the Re = 8000, 10000, and 12000, respectively, and the maximum Nu increases from 358.540 to 478.821. Compared with the design with the maximum thermal performance, the best compromise solution from multi-objective optimization is determined at Re = 8000, 10000, and 12000, showing improved flow resistance of 83.917%, 85.465%, and 84.473%, but with sacrificed thermal performance of 36.754%, 37.088%, and 35.005%, respectively.