Characterization of the secondary flow in turbulent rectangular ducts with varying aspect ratio

Authors: Vinuesa, R., Schlatter, P., Nagib, H.M.
Document Type: Article
Pubstate: Published
Journal: 9th International Symposium on Turbulence and Shear Flow Phenomena (TSFP-9)
Year: 2015


Direct numerical simulations of turbulent duct flows with width-to-height ratios 1, 3, 5, 7 and 10, at a friction Reynolds number Ret,c '180, are carried out with the spectral element code Nek5000. The aim of these simulations is to gain insight into the kinematics and dynamics of Prandtl’s secondary flow of second kind, and its impact on the flow physics of wall-bounded turbulence. The secondary flow is characterized in terms of the cross-plane mean kinetic energy K = (V2+W2)/2, and its variation in the spanwise direction of the flow. Our results show that averaging times of at least 3,000 time units are required to reach a converged state of the secondary flow, which extends up to z ' 5h from the side walls. We also show that if the duct is not wide enough to accommodate the whole extent of the secondary flow, then its structure is modified by means of a different spanwise distribution of energy. The kinetic energy of the secondary flow for z > 5h in aspect ratios 7 and 10 exhibits a decaying level of energy, and the rate of decay is approximately hKyzi T?1 A . This is the same rate of decay observed in a spanwise-periodic simulation, which suggests that at the core, hKiyz behaves as a random variable with zero mean, with rate of decay consistent with central limit theorem theory. Non-stationary effects of the secondary flow may persist into the core for all the aspect ratios we have run so far, and may interact with the dynamics of the nominally homogeneous flow that would exist in a channel. The non-stationary effects will be presented and further discussed in the Symposium. Note that these conclusions are limited to the low Reynolds number range under consideration, and additional data will be necessary to assess Reynolds number effects.