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Numerical study of flow through and around a circular array of cylinders

Published online by Cambridge University Press:  27 May 2011

A. NICOLLE  and
I. EAMES
A. NICOLLE*
Affiliation:
University College London, Torrington Place, London WC1E 7JE, UK
I. EAMES
Affiliation:
University College London, Torrington Place, London WC1E 7JE, UK
*
†Email address for correspondence: a.nicolle@ucl.ac.uk
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Abstract

This paper describes a study of the local and global effect of an isolated group of cylinders on an incident uniform flow. Using high resolution two-dimensional computations, we analysed the flow through and around a localised circular array of cylinders, where the ratio of array diameter (DG) to cylinder diameter (D) is 21. The number of cylinders varied from NC = 7 to 133, and they were arranged in a series of concentric rings to allow even distribution within the array with an average void fraction φ = NC(D/DG)2, which varied from 0.016 to 0.30. The characteristic Reynolds number of the array was ReG = 2100. A range of diagnostic tools were applied, including the lift/drag forces on each cylinder (and the whole array), Eulerian and Lagrangian average velocity within the array, and the decay of maximum vorticity with distance downstream. To interpret the flow field, we used vorticity and the dimensionless form of the second invariant of the velocity gradient tensor. A mathematical model, based on representing the bodies as point forces, sources and dipoles, was applied to interpret the results. Three distinct flow regimes were identified. For low void fractions (φ < 0.05), the cylinders have uncoupled individual wake patterns, where the vorticity is rapidly annihilated by wake intermingling downstream and the forces are similar to that of an isolated cylinder. At intermediate void fractions (0.05 < φ < 0.15), a shear layer is generated at the shoulders of the array and the force acting on the cylinders is steady. For high void fractions (φ > 0.15), the array generates a wake in a similar way to a solid body of the same scale. For low void fraction arrays, the mathematical model provides a reasonable assessment of the forces on individual bodies within the array, the Eulerian mean velocity and the upstream velocity field. While it broadly captures the change in the rate of decay of the maximum vorticity magnitude Ωmax downstream, the magnitude is underpredicted.

JFM classification

Mathematical Foundations: Computational methods Mathematical Foundations: General fluid mechanics Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 679 , 25 July 2011 , pp. 1 - 31
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Ball, D. J. & Hall, C. D. 1980 Drag of yawed pile groups at low Reynolds number. ASCE J. R. Aero. Soc. 90, 128–38.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Mechanics. Cambridge University Press.Google Scholar
Bhattacharyya, S., Dhinakaran, S. & Khalili, A. 2006 Fluid motion around and through a porous cylinder. Chem. Engng Sci. 61, 4451–4461.CrossRefGoogle Scholar
Blackburn, H. M. 2006 Effect of blockage on critical parameters for flow past a circular cylinder. Intl J. Numer. Meth. Fluids 50, 987–1001.Google Scholar
Castro, I. P. 1971 Wake characteristics of two-dimensional perforated plates normal to an air-stream. J. Fluid Mech. 46, 599–609.CrossRefGoogle Scholar
Chang, C. C., Yang, S. H. & Chu, C. C. 2008 A many-body force decomposition with applications to flow about bluff bodies. J. Fluid Mech. 600, 95–104.CrossRefGoogle Scholar
Chorin, A. J. 1968 Numerical solution of Navier–Stokes equations. Math. Comput. 22, 745–762.CrossRefGoogle Scholar
Codina, R., Coppola-Owen, H., Nithiarasu, P. & Liu, C.-B. 2006 Numerical comparison of CBS and SGS as stabilization techniques for the incompressible Navier–Stokes equations. Intl J. Numer. Meth. Engng 66, 1672–1689.CrossRefGoogle Scholar
Clift, R., Grace, J. & Weber, M. E. 1978 Bubbles, Droplets and Particles. Dover Publications. p. 381.Google Scholar
Davidson, P. A. 2004 Turbulence: An Introduction for Scientists and Engineers. Oxford University Press.Google Scholar
Eames, I., Hunt, J. C. R. & Belcher, S. E. 2004 Inviscid mean flow through and around groups of bodies. J. Fluid Mech. 515, 371–389.CrossRefGoogle Scholar
Eames, I., Roig, V., Hunt, J. C. R. & Belcher, S. E. 2007 Vorticity annihilation and inviscid blocking in multibody flows. Nato Meeting Ukraine May 69.Google Scholar
Huang, Z., Kawall, J. G. & Keffer, J. F. 1996 Development of structure within the turbulent wake of a porous body. Part 2. Evolution of the three-dimensional features. J. Fluid Mech. 329, 117–136.CrossRefGoogle Scholar
Hunt, J. C. R. & Eames, I. 2002 The disappearance of laminar and turbulent wakes in complex flows. J. Fluid Mech. 457, 111–132.CrossRefGoogle Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream and convergence zones in turbulent flows. In Proc. 1988 Summer Program, Stanford NASA. Centre for Turb. Res., CTR-S88.Google Scholar
Jeong, J. & Hussain, F. 2006 On the identification of a vortex. Fluid Dyn. Res. 28, 449–464.Google Scholar
Kim, H.-B. & Lee, S.-J. 2001 Hole diameter effect on flow characteristics of wake behind porous fences having the same porosity. J. Fluid Mech. 285, 69–94.Google Scholar
Legendre, D., Borée, J. & Magnaudet, J. 1998 Thermal and dynamic evolution of a spherical bubble moving steadily in a superheated or subcooled liquid. Phys. Fluids 10, 1256.Google Scholar
Malan, A. G., Lewis, R. W. & Nithiarasu, P. 2002 An improved unsteady, unstructured, artificial compressibility, fnite volume scheme for viscous incompressible flows. Part II. Application. Intl J. Numer. Meth. Engng 54, 715–729.Google Scholar
Moulinec, C., Hunt, J. C. R. & Nieuwstadt, F. T. M. 2004 Disappearing wakes and dispersion in numerically simulated flows through tube bundles. Flow Turbul. Combust. 73, 95–116.CrossRefGoogle Scholar
Nicolle, A. 2009 Flow through and around groups of bodies. PHD thesis, University College London.Google Scholar
Nithiarasu, P. & Zienkiewicz, O. C. 2005 Analysis of an explicit and matrix free fractional step method for incompressible flows. Comput. Meth. Appl. Mech. Engng 195, 5537–5551.CrossRefGoogle Scholar
Pearcey, H. H., Sing, S., Cash, R. F. & Matten, R. B. 1982 Interference effects on the drag loading for groups of cylinders in uni-directional flow. Feltham UK Rep. NMI R130.Google Scholar
Ramon, C. 2002 Stabilized finite element approximation of transient incompressible flows using orthogonal subscales. Comput. Meth. Appl. Mech. Engng 191, 4295–4321.Google Scholar
Roig, V. & Tournemine, L. de 2007 Measurement of interstitial velocity of homogeneous bubbly flows at low to moderate void fraction. J. Fluid Mech. 572, 87–110.CrossRefGoogle Scholar
de Sampaio, P. A. B., Lyra, P. R. M., Morgan, K. & Weatherill, N. P. 1993 Petrov-Galerkin solutions of the incompressible Navier–Stokes equations in primitive variables with adaptive remeshing. Comput. Meth. Appl. Mech. Engng 106, 143–178.CrossRefGoogle Scholar
Singh, S. P. & Mittal, S. 2004 Flow past a cylinder: shear layer instability and drag crisis. Intl J. Numer. Meth. Fluids 47, 75–98.Google Scholar
Taylor, P. H. 1991 Current blockage: reduced force on offshore space-frame structures. Offshore Technol. Conf. Paper no. OTC 6519.Google Scholar
Yu, P., Zeng, Y., Lee, T. S., Bai, H. X. & Low, H. T. 2010 Wake structure for flow past and through a porous square cylinder. Intl J. Heat Fluid Flow 31, 141–153.Google Scholar
Zdravkovich, M. M. 1997 Flow around Circular Cylinders: Applications, vol 1. Oxford University Press.Google Scholar
Zienkiewicz, O. C. & Codina, R. 1995 A general algorithm for compressible and incompressible flow. Part I. The split, characteristic-based scheme. Intl J. Numer. Meth. Fluids 20, 869–885.CrossRefGoogle Scholar
Zienkiewicz, O. C., Taylor, R. L & Nithiarasu, P. 2005 The Finite Element Method for Fluid Dynamics, 6th edn. Elsevier Butterworth Heinemann.Google Scholar