Pressure losses for turbulent flow through bends in series

The pressure loss caused by a single isolated bend, which receives a fully developed flow and allows the flow to return to a fully developed state in its downstream tangent, is well documented and understood. However, when two or more bends are separated by a length insufficient to restore fully developed flow, the truncation of the pressure loss occurring downstream of the first bend and the distorted flow received by the second bend prevent the extrapolated use of single-bend data for the two-bend case. Using numerical simulation, a comprehensive investigation of the pressure losses caused by two-bend combinations was performed. Two in-plane bend combinations, having a “U” and “S” shape, and an out-of-plane bend combination were examined. For each bend combination, simulations were performed for many separating lengths ranging from zero to 100 pipe diameters for Reynolds numbers of 2· 10⁵, 5·10⁴, and 1·10⁴. For the “U” combination, the two-bend pressure loss decreased monotonically as the separating distance decreased. For the “S” and out-of-plane configurations, the pressure loss was at a minimum when the separating length was between three and five pipe diameters. This is consistent with the existing results from the highest quality experiments on the topic. In addition to results, the present work presents a fundamentals-based comprehensive explanation of the observed pressure loss trends using dimensionless quantities to measure the distortion of the flow at cross sections within the bend combination.