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Secondary flow in turbulent ducts with increasing aspect ratio

R. Vinuesa1,*, P. Schlatter1, and H. M. Nagib2

  • 1Linné FLOW Centre, KTH Mechanics and Swedish e-Science Research Centre (SeRC), Stockholm SE-100 44, Sweden
  • 2MMAE Department, Illinois Institute of Technology, Chicago, Illinois IL 60616, USA

  • *rvinuesa@mech.kth.se
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Phys. Rev. Fluids 3, 054606 – Published 17 May, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.054606

Abstract

Direct numerical simulations of turbulent duct flows with aspect ratios 1, 3, 5, 7, 10, and 14.4 at a center-plane friction Reynolds number Reτ,c≃180, and aspect ratios 1 and 3 at Reτ,c≃360, were 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 the second kind and its impact on the flow physics of wall-bounded turbulence. The secondary flow is characterized in terms of the cross-plane component of the mean kinetic energy, and its variation in the spanwise direction of the flow. Our results show that averaging times of around 3000 convective time units (based on duct half-height h) are required to reach a converged state of the secondary flow, which extends up to a spanwise distance of around ≃5h measured 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 as reflected through a different spanwise distribution of energy. Another confirmation of the extent of the secondary flow is the decay rate of kinetic energy of any remnant secondary motions for zc/h>5 (where zc is the spanwise distance from the corner) in aspect ratios 7, 10, and 14.4, which exhibits a decreasing level of energy with increasing averaging time ta, and in its rapid rate of decay given by ∼ta−1. This is the same rate of decay observed in a spanwise-periodic channel simulation, which suggests that at the core, the kinetic energy of the secondary flow integrated over the cross-sectional area, 〈K〉yz, behaves as a random variable with zero mean, with rate of decay consistent with central limit theorem. Long-time averages of statistics in a region of rectangular ducts extending about the width of a well-designed channel simulation (i.e., extending about ≃3h on each side of the center plane) indicate that ducts or experimental facilities with aspect ratios larger than 10 may, if properly designed, exhibit good agreement with results obtained from spanwise-periodic channel computations.

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Phys. Rev. Fluids 3, 054606– Published 17 May, 2018
  • Received 15 December 2017
Article part of CHORUS
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