Numerical Study of Dean Vortices in U-tubes of Finite Aspect Ratios

Abstract

The flow in curved channels or pipes is fairly complex. As a result of centrifugal forces interacting with inertia and viscous forces, secondary flows are established. Above some critical Reynolds number, these secondary flows may include additional pairs of smaller counter-rotating vortices near the outer concave wall of the pipe.For pipes with rectangular cross-sections, multiple pairs of these vortices may be observed, typically arranged spanwise along the outer concave wall. Such vortices are known as Dean vortices. Theoretically, the phenomenon is considered as a complex bifurcation problem with multiple solutions.First, an extensive literature survey on the topic is conducted. Next, the numerical workings are detailed, and by employing a??special techniquesa??, the bifurcated solutions are obtained using a commercial computational fluid dynamics package. Validation is performed with available experimental data.The analysis is advanced further by investigating the downstream flow past the bend of a U-tube. From these studies, multiple cell solutions are obtained drawing analogy with the G??rtler problem. The discrepancies between experimental and numerical results on the critical Dean number are further investigated with substantiating findings to justify the obtained results. Finally, the gradual transition from multiple vortex pairs to a single pair of counter-rotating vortices once the flow leaves the bend, which is attributed to a a??post-centrifugala?? effect, is reported.