Comparisons of flow around the spaced and bundled pipes at various gap ratios and Reynolds numbers

This study numerically investigates the hydrodynamic characteristics of two piggyback pipeline configurations, spaced and bundled pipe system, over a Reynolds number range of Re = 40–150 and gap ratios of G* = 0.1–0.5. Three key findings emerge, with direct implications for offshore pipeline design and stability assessment. First, for the spaced configuration, the gap ratio fundamentally governs the flow regime: single-bluff-body behavior at small gaps transitions to separated flow with independent vortex streets at larger gaps. Within each regime, the Reynolds number modulates the drag coefficient, vortex-shedding modes (2S, 2P, and P + S), and the phase shifts in inter-pipe force fluctuations. A notable trend reversal is observed in the Strouhal number: at small gaps, St decreases with increasing Re, whereas at large gaps, St increases with Re. This reversal is attributed to the competing effects of gap-flow acceleration and shear-layer instability, which alter the vortex formation length in opposite ways depending on the gap ratio. Second, for the bundled configuration, the hydrodynamic response is governed by the interplay between geometric bias and shear-layer dynamics. The mean lift coefficient exhibits a non-monotonic variation with Re at G* = 0.3 and 0.5, peaking around Re = 100 before decreasing. This behavior reflects a competition between the geometric asymmetry, which imposes a persistent pressure imbalance, and the transition in vortex shedding modes (from 2S to 2P), which redistributes the time-averaged surface pressure. The drag coefficient increases monotonically with both Re and gap ratio, while the Strouhal number decreases systematically as the gap widens. Third, a comparative analysis reveals that at the smallest gap (G* = 0.1), both configurations exhibit similar hydrodynamic behavior, with the secondary pipe fully immersed in the main pipe's wake. As the gap increases, their responses diverge markedly: the spaced configuration transitions to independent vortex shedding from each pipe, while the bundled configuration maintains a single-bluff-body character but experiences periodic surface reattachment on the secondary pipe. This results in continuously increasing drag, significantly larger lift fluctuations, and a consistently lower vortex-shedding frequency. Collectively, these findings clarify the parametric dependencies and underlying mechanisms governing the hydrodynamic responses of the two piggyback configurations. The quantitative comparisons of force coefficients and Strouhal numbers provide a robust basis for configuration selection and fatigue life assessment in engineering design.