Numerical simulations were performed with the open-source CFD software OpenFOAM to investigate the ability of several configurations of short-length twisted tube geometries with non-circular cross section connected to tubes with circular cross section to induce a swirling flow. The heat transfer and the pressure drop linked to the generated swirling flow are also calculated. The swirling flow is modeled using a k-ω SST turbulence model with a low-Reynolds approach. It is shown that a short-length twisted tube with an elliptical cross section (STE) is able to generate a swirling flow, but its intensity greatly depends on its twist pitch and its aspect ratio. The lower the aspect ratio, the higher the swirl intensity. For a Reynolds number ranging from 10,000 to 100,000, the results reveal that compared to a plain tube, the STE with the lowest aspect ratio achieves enhancing the heat transfer from 22 to 90% at the cost of an increased pressure drop of, respectively, 63 and 129%. The second part of the study is focused on a short-length twisted tube with a three-lobed cross section, and the results reveal that the generated swirling flow is even more intense than with the STE and that the heat transfer enhancement goes from 30 to 105% at the cost of an increased pressure drop from 137 to 180%.