Effects of aspect ratio on turbulent elliptical pipe flow and structures

Turbulent flows within elliptical pipes of varying aspect ratios (AR) have been studied using direct numerical simulations. To understand the AR effects on turbulence statistics and structures, three elliptical pipe flow cases (of AR=1.5:1, 2:1, and 3:1) have been investigated and compared with a circular pipe flow case (of AR=1:1). As a result of the varying wall curvature of elliptical pipes, large-scale secondary flows appear in the cross-stream direction as two pairs of counter-rotating vortices at relatively small AR values, which significantly impact the turbulence statistics of the flow. As the AR value increases, it is interesting to observe that the mean cross-stream vortical structures become increasingly stretched along the direction of the semi-major axis, eventually splitting into four pairs of smaller vortices at the largest AR value tested. Furthermore, as the AR value increases, a significant trend toward turbulence suppression is observed at the ends of the major axis, where the formation and strength of hairpin structures reduce monotonically. Along the semi-major axis, it is discovered that the turbulence kinetic energy levels (as indicated by the three components of the premultiplied velocity spectra) reduce dramatically across all wavelengths, while their modes migrate monotonically toward larger wavelengths as the AR value increases. The characteristics of the flow field under the influence of a varying AR are investigated in both physical and spectral spaces in terms of the mean and instantaneous flows, turbulence intensities, Reynolds stress budgets, and coherent flow structures.