Turbulence structure and budgets in curved pipes

Abstract

Turbulent flow in curved pipes was investigated by Direct Numerical Simulation. Three curvatures δ (pipe radius a/curvature radius c) were examined: δ=0 (straight pipe), simulated for validation and comparison purposes; δ=0.1; and δ=0.3. The friction velocity Reynolds number (based on the pipe radius a) was 500 in all cases, yielding bulk Reynolds numbers of ∼17,000, ∼15,000 and ∼12,000 for δ=0, 0.1 and 0.3, respectively. The computational domain was ten pipe radii in length and was resolved by up to 20×106 hexahedral finite volumes. The time step was chosen equal to a wall time unit; 1 Large Eddy TurnOver Time (LETOT) was thus resolved by 500 time steps and simulations were typically protracted for 20 LETOT’s, the last 10 being used to build turbulence statistics and budgets.In curved pipes, time mean results showed Dean circulation and a strong velocity stratification in the curvature direction, as in laminar flow; turbulent fluctuations were highest in the outer bend region, whereas the flow near the inner wall was almost laminar. Significant turbulence levels were confined to a near-wall layer narrower than in the straight pipe. Near-wall streamwise velocity and wall shear stress exhibited the streak structure typical of turbulent channel flows only along the outer wall, while on the inner wall they exhibited a flat and low-level distribution. As the curvature increased, fluctuations in the plane of the cross section increased in intensity, following the trend of the time mean secondary flow, whereas axial (streamwise) fluctuations became weaker. Overall turbulence levels decreased with the curvature and were lower in a curved pipe than in the straight pipe. Turbulence budgets over the cross section confirmed that in curved pipes production and other budget terms are comparable with those in the straight pipe (or even higher) in the outer bend region, whereas they rapidly decay as one moves towards the inner side. They also indicated that, in curved pipes, convection terms play a significant role in the turbulence budget, especially in the regions of the Dean vortices.