Hostname: page-component-7c8c6479df-8mjnm Total loading time: 0 Render date: 2024-03-27T13:01:00.703Z Has data issue: false hasContentIssue false

Force acting on a square cylinder fixed in a free-surface channel flow

Published online by Cambridge University Press:  04 September 2014

Z. X. Qi
Affiliation:
University College London, Torrington Place, London WC1E 7JE, UK
I. Eames*
Affiliation:
University College London, Torrington Place, London WC1E 7JE, UK
E. R. Johnson
Affiliation:
University College London, Torrington Place, London WC1E 7JE, UK
*
Email address for correspondence: i.eames@ucl.ac.uk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We describe an experimental study of the forces acting on a square cylinder (of width $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}b$) which occupies 10–40 % of a channel (of width $w$), fixed in a free-surface channel flow. The force experienced by the obstacle depends critically on the Froude number upstream of the obstacle, ${\mathit{Fr}}_1$ (depth $h_1$), which sets the downstream Froude number, ${\mathit{Fr}}_2$ (depth $h_2$). When ${\mathit{Fr}}_1<{\mathit{Fr}}_{1c}$, where ${\mathit{Fr}}_{1c}$ is a critical Froude number, the flow is subcritical upstream and downstream of the obstacle. The drag effect tends to decrease or increase the water depth downstream or upstream of the obstacle, respectively. The force is form drag caused by an attached wake and scales as $\overline{F_{D}}\simeq C_D \rho b u_1^2 h_1/2$, where $C_D$ is a drag coefficient and $u_1$ is the upstream flow speed. The empirically determined drag coefficient is strongly influenced by blocking, and its variation follows the trend $C_D=C_{D0}(1+C_{D0}b/2w)^2$, where $C_{D0}=1.9$ corresponds to the drag coefficient of a square cylinder in an unblocked turbulent flow. The r.m.s. lift force is approximately 10–40 % of the mean drag force and is generated by vortex shedding from the obstacle. When ${\mathit{Fr}}_1={\mathit{Fr}}_{1c}\, (<1)$, the flow is choked and adjusts by generating a hydraulic jump downstream of the obstacle. The drag force scales as $\overline{F}_D\simeq C_K \rho b g (h_1^2-h_2^2)/2$, where experimentally we find $C_K\simeq 1$. The r.m.s. lift force is significantly smaller than the mean drag force. A consistent model is developed to explain the transitional behaviour by using a semi-empirical form of the drag force that combines form and hydrostatic components. The mean drag force scales as $\overline{F_{D}}\simeq \lambda \rho b g^{1/3} u_1^{4/3} h_1^{4/3}$, where $\lambda $ is a function of $b/w$ and ${\mathit{Fr}}_1$. For a choked flow, $\lambda =\lambda _c$ is a function of blocking ($b/w$). For small blocking fractions, $\lambda _c= C_{D0}/2$. In the choked flow regime, the largest contribution to the total drag force comes from the form-drag component.

Type
Papers
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© 2014 Cambridge University Press

References

Awbi, H. B. 1978 Wind-tunnel-wall constraint on two-dimensional rectangular-section prisms. J. Ind. Aerodyn. 3, 285306.CrossRefGoogle Scholar
Azinfar, H. & Kells, J. A. 2009 Flow resistance due to a single spur dike in an open channel. J. Hydraul. Res. 47, 755763.Google Scholar
Benjamin, T. B. 1956 On the flow in channels when rigid obstacles are placed in the stream. J. Fluid Mech. 1, 227248.Google Scholar
Betz, A. 1925 A method for the direct determination of profile drag. Z. Flugtech. Motorluftschiffahrt 16, 4244 (in German).Google Scholar
Brocchini, M. & Peregrine, D. H. 2001 The dynamics of strong turbulence at free surfaces. Part 1. Description. J. Fluid Mech. 449, 225254.Google Scholar
Fenton, J. D. 2003 The effects of obstacles on surface levels and boundary resistance in open channels. In Proceedings of the 30th IAHR World Congress (Thessaloniki, Greece, 2003) (ed. Ganoulis, J. & Prinos, P.), vol. C2, pp. 916. Aristoteleio Panepistimio Thessalonikis.Google Scholar
Fenton, J. D. 2008 Obstacles in streams and their roles as hydraulic structures. In Hydraulic Structures – Proceedings of the 2nd International Junior Researcher and Engineer Workshop on Hydraulic Structures (Pisa, Italy, 30 July–1 August 2008) (ed. Pagliara, S.), pp. 1522. Pisa University Press.Google Scholar
Henderson, F. M. 1966 Open Channel Flow. Macmillan.Google Scholar
Maskel, E. C.1963 A theory of the blockage effects on bluff bodies and stalled wings in a closed wind tunnel. Tech. Rep. Reports and Memoranda No. 3400, Aeronautical Research Council, London.Google Scholar
Massey, B. S. & Ward-Smith, J. 1998 Mechanics of Fluids. Taylor & Francis.Google Scholar
Nagler, F. A. 1918 Obstruction of bridge piers to the flow of water. Trans. ASCE 82, 334395.Google Scholar
Nicolle, A. & Eames, I. 2011 Numerical study of flow through and around a circular array of cylinders. J. Fluid Mech. 679, 131.Google Scholar
Raju, K. G. R., Rana, O. P. S., Asawa, G. L. & Pillai, A. S. N. 1983 Rational assessment of blockage effect in channel flow past smooth circular cylinders. J. Hydraul. Res. 21, 289302.Google Scholar
Sharify, E. M., Saito, H., Taikan, H., Takahashi, S. & Arai, N.2012 Experimental and numerical study of blockage effects on flow characteristics around a square-section cylinder. In ISEM-ACEM-SEM-7th ISEM Conference, Taipei, Taiwan.Google Scholar
Sohankar, A., Norberg, C. & Davidson, L. 1999 Large eddy simulation of flow past a square cylinder. Trans. ASME J. Fluids Engng 122, 3947.Google Scholar
Tamura, T. & Miyagi, T. 1999 The effect of turbulence on aerodynamic forces on a square cylinder with various corner shapes. J. Wind Engng Ind. Aerodyn. 127, 657662.Google Scholar
Yarnell, D. L.1934a Pile trestles as channel obstructions. Tech. Rep. 429, US Department of Agriculture, Washington.Google Scholar
Yarnell, D. L.1934b Bridge piers as channel obstructions. Tech. Rep. 442, US Department of Agriculture, Washington.Google Scholar