Laminar flow and heat transfer in U-bends: The effect of secondary flows in ducts with partial and full curvature.

The present study numerically explores the flow and heat transfer in “U-type” curved pipes of either partial or full curvature, which are often used as integral parts of heat exchangers and heat sinks in industrial applications such as solar thermal systems, among many others. Specifically, the case of a high-Prandtl-number Newtonian fluid (thermal oil) in laminar forced convection inside partially and fully curved “U-bends” is investigated, in order to illustrate the effect of the generated secondary flows on the various local and global scales. The 3D steady-state simulations are performed using the free and open source computational fluid dynamics software “OpenFOAM”. The analysis of the computational results is initially based on data at selected characteristic locations of interest; they are properly established and further explored by extracting internal field variables, in the form of 2D contours of quantities of interest, such as temperature and vorticity. A parametric study on the flow rate and curvature impact, namely in terms of increasing Re and De numbers ( Re  = 100, 1000, 2000), on the heat transfer process inside the U-bends is conducted comparatively for both geometries. The presence of secondary flows is confirmed and the differences between the geometries under investigation are visually illustrated. For moderate and high Re numbers, the presence of multiple counter-rotating secondary cells is generally observed, while the partially curved U-bend (“composite”) displays a more complex flow topology. This behavior is projected on heat transfer through the examination of temperature distribution on inner and outer arcs of both geometries. It is shown that the composite bend causes an abrupt decrease and oscillations on temperature distributions, which are found to be related with phenomena like flow impingement, separation and re-attachment. The Pr number effect is illustrated through a comparison with a lower Pr fluid and its impact is demonstrated both inside and downstream of the U-bends. The averaged Nusselt distribution along the length of both curved ducts further highlights the impact of these phenomena on local heat transfer and provides initial evidence in favor of the composite bend. The overall performance of the investigated curved geometries is compared based on a “performance factor” criterion and a superior performance of the composite U-bend is further established, attaining a value of almost 45% for higher flow rates. Finally, the effect of each U-bend on the straight pipe downstream of their respective exit is quantified. High divergence from the regular “combined hydrodynamic and thermal entrance flow” is found for the forced convection inside the downstream pipe. A characteristic overshoot of the downstream-to-upstream ratio Nusselt number is found for moderate and higher flow rates at small lengths from entrance (z*). The partially curved U-bend downstream effect seems to be greater for the investigated cases of Re  = 100, 2000, while the fully curved outperforms the composite for the moderate Re case ( Re  = 1000). The source of this discrepancy cannot be clearly identified through this work and further investigation is needed on this matter. All in all, the simulations performed here show that partially curved U-bends can potentially be advantageous, in terms of performance, compared to the standard fully-curved pipes for laminar forced convection applications. These results can provide a good starting point for the optimal design of such ducts for several heat transfer operations. [ABSTRACT FROM AUTHOR]