Evolution of turbulence characteristics from straight to curved pipes

• First study of bent pipes using well resolved DNS at higher Re (Reτ = 400) and curvature (κ = 0.1).
• Careful validation of results with literature, and discussion of the new data.
• Complex behaviour of the secondary flow (Dean vortices), showing distinction between mild and strong curvature.
• Full Reynolds-stress budgets for bent pipe computed for the first time, particularly important for turbulence modelling.
• Confirmation of sub-straight drag coefficient for mildly curved pipes (κ = 0.01).

Fully developed, statistically steady turbulent flow in straight and curved pipes at moderate Reynolds numbers is studied in detail using direct numerical simulations (DNS) based on a spectral element discretisation. After the validation of data and setup against existing DNS results, a comparative study of turbulent characteristics at different bulk Reynolds numbers Reb = 5300 and 11,700, and various curvature parameters κ = 0, 0.01, 0.1 is presented. In particular, complete Reynolds-stress budgets are reported for the first time. Instantaneous visualisations reveal partial relaminarisation along the inner surface of the curved pipe at the highest curvature, whereas developed turbulence is always maintained at the outer side. The mean flow shows asymmetry in the axial velocity profile and distinct Dean vortices as secondary motions. For strong curvature a distinct bulge appears close to the pipe centre, which has previously been observed in laminar and transitional curved pipes at lower Reb only. On the other hand, mild curvature allows the interesting observation of a friction factor which is lower than in a straight pipe for the same flow rate.All statistical data, including mean profile, fluctuations and the Reynolds-stress budgets, is available for development and validation of turbulence models in curved geometries.