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A steady Newtonian fluid flow through annular region in curved pipes is studied in this paper. The flow takes place due to an axial pressure gradient and it is three-dimensional in nature. The equations governing the flow are highly coupled and nonlinear. The solutions are obtained, analytically, using a regular perturbation method. The effects of curvature ratio (δ) , Reynolds number (Re) and the radius ratio (l) on the axial velocity and stream function are presented graphically. It is observed that, along with curvature ratio and Reynolds number, radius ratio highly affects the fluid flow in annular curved pipes. [ABSTRACT FROM AUTHOR]

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]

Transition to turbulent flow in a curved pipe has been well studied through experiments and numerical simulations. Numerical simulations often use a helical pipe with an infinite length such that the inlet and outlet boundary conditions can be modelled as periodic which greatly reduces computational time. In this study, we examined a finite length curved pipe with Poiseuille flow imposed at the inlet and a stress-free boundary condition at the outlet. Direct numerical simulation of the Navier-Stokes equations for rigid walls and a Newtonian fluid was performed using nek5000. Straight extensions were added to the inlet and outlet such to diminish the impact of boundary conditions on the flow field in the region with curvature. The examined model has a pipe radius of curvature that is three times the pipe radius. The model has ∼355 million nodes and required an order of magnitude greater computational time when compared with an infinite length curved pipe. Results show that the critical Reynolds number, the lowest value with instabilities present in the flow, is much greater than that of a straight pipe and occurs near Re=5000-5200. This is larger than the critical Reynolds number typically reported for an infinite length curved pipe (Re=4200-4300). [ABSTRACT FROM AUTHOR]

A serpentine pipe is a sequence of parallel straight pipe segments connected by U-bends. Its geometry is fully characterized by pipe radius, a , bend curvature radius, c and length of the straight segments, l . The repeated curvature inversion forces the recirculation (secondary flow) pattern to switch between two specular configurations, which may enhance mixing and heat or mass transfer with respect to a constant-curvature pipe at the cost of an increase in pressure drop. In the present work, fully developed laminar flow and heat transfer in serpentine pipes were investigated by numerical simulation. The curvature δ = a / c was made to vary between 0.1 and 0.5 while the parameter γ = l / c was made to vary between 0 and 8; for each geometry, the friction velocity Reynolds number Re τ = u τ a / ν was made to vary between a very low value (5), yielding almost creeping flow, and the highest value Re τ ∗ still yielding steady laminar flow (∼35–40 in most cases). For Re τ ≤ Re τ ∗ results were obtained for values of the Prandtl number between 1 and 100; predicted values of the friction coefficient and of the Nusselt number were compared with experimental results and correlations proposed in the literature. For Re τ > Re τ ∗ convergence to steady flow was not achieved and an oscillatory behaviour of the solution was observed, indicating a transition to unsteady regimes which deserves a more focused study. [ABSTRACT FROM AUTHOR]