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Drag on pairs of square section obstacles in free-surface flows

Francis H. Robertson* and Gregory F. Lane-Serff†

  • School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester M13 9PL, United Kingdom

  • *Present address: School of Engineering, The University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom.
  • †g.f.lane-serff@manchester.ac.uk
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Phys. Rev. Fluids 3, 123802 – Published 18 December, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.123802

Abstract

The drag on pairs of square obstacles (of side D) in open channel flow is measured in experiments using a laboratory flume. The depth is uniform across the obstacles and the conditions in the flume are subcritical, with Froude number Fr<0.59, Reynolds number Re = 4800 to 21900, and turbulence intensity IT∼8 to 10%. The drag coefficient for an isolated square obstacle is found to be CD=2.11, in agreement with previous studies, and independent of Re (for the range covered here). The root-mean-square variation in the drag coefficient for the single obstacle decreased monotonically with Re, defined in terms of hydraulic radius, and approached 0.241 at high Re in agreement with previous research. For two obstacles, standard tandem and side-by-side arrangements are studied first, followed by a full range of relative positions covering −5≤sx/D≤20 in the downstream direction and 0≤sy/D≤7.0 in the cross-stream direction. The lowest drag coefficients are observed when the downstream obstacle is shielded directly behind the upstream obstacle (tandem arrangement) when negative drag coefficients are found. The largest drag coefficients are observed for nearly side-by-side arrangements, with the peak values found to be for the slightly upstream obstacle of a pair (sx/D=−1). The blockage ratio (D/B, the relative size of the obstacle compared to the channel width) is found to be an important factor. For D/B = 12.7% the largest drag coefficient is CD=3.82, while for D/B = 6.3% the largest value is CD=2.85. For tandem obstacles, the drag on one obstacle can largely be accounted for by the change in flow speed induced by the other obstacle, except at small separations (|sx/D|<3). The results will be useful in any applications where the force on multiple obstacles is required, such as the design of marine or riverine structures, or flood flows past buildings and vegetation.

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Phys. Rev. Fluids 3, 123802– Published 18 December, 2018
  • Received 21 August 2017
  • Revised 12 September 2018
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