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An unsteady wake-source model for flow past an oscillating circular cylinder and its implications for Morison's equation

Published online by Cambridge University Press:  26 April 2006

Y. T. Chew ,
H. T. Low ,
S. C. Wong  and
K. T. Tan
Y. T. Chew
Affiliation:
Department of Mechanical and Production Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511
H. T. Low
Affiliation:
Department of Mechanical and Production Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511
S. C. Wong
Affiliation:
Department of Mechanical and Production Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511
K. T. Tan
Affiliation:
Department of Mechanical and Production Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511
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Abstract

A potential-flow modelling of flow past an oscillating circular cylinder with separated wake is developed here based on Parkinson & Jandali's (1970) wake-source model for steady flow. The phase-averaged pressure distributions, the in-line force coefficients, as well as the drag and added-mass coefficients, for an in-line oscillating circular cylinder in a steady free-stream flow are computed using the present ‘unsteady wake-source model’. The results show that Morison's equation is in some cases a satisfactory model in the study of unsteady bluff-body aerodynamics.

The two-dimensional incompressible potential-flow model simulates the effect of flow separation in unsteady flow by placing surface sources, with time-dependent strength and angular positions on the rear wetted surface of the body, and downstream sinks to form a closed wake model in the transformed plane. The unsteady Bernoulli equation is used to obtain the time-dependent pressure distributions over the front wetted surface, from which the in-line force coefficients are obtained through integration.

The in-line force equation obtained from the present model is shown to be comprised of an uncoupled drag term and inertia terms. The corresponding hydrodynamie coefficients obtained for the case of oscillatory flow are also more realistic than those obtained in a potential-flow calculation without flow separation which gives a drag coefficient of zero and a constant inertia coefficient of 2.0. The in-line force equation is reduced to the familiar Morison's equation with some simplifications and thus provides some support to the much criticized Morison's equation in the study of unsteady separated flow.

Another interesting feature of the present model is that it enables the calculation of instantaneous drag and inertia coefficients which have not been successfully obtained previously. In the cases considered here, the variations of drag and inertia coefficients over a cycle are shown to be small and thus the Morison's equation using mean coefficients is shown to predict the in-line forces rather precisely.

The present model was compared with experimental measurements obtained by oscillating a 0.1 m diameter circular cylinder along the direction of free-stream flow. The pressure distributions and in-line force coefficients agree well with the experimental measurements for velocity ratio rω/U∞ up to 0.25, reduced velocity U∞T/d down to 50 and Keulegan—Carpenter number 2πr/d up to 17, where r, ω, T, U∞ and d are the amplitude of oscillation, angular frequency, period of oscillation, free-stream velocity and diameter of the cylinder respectively. The computed drag and inertia coefficients also agree well with those obtained experimentally by previous investigators.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 240 , July 1992 , pp. 627 - 650
Copyright
© 1992 Cambridge University Press

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References

Archibald, R. S. & Robins, A. W. 1952 A method for the determination of the time lag in pressure measuring systems incorporating capillaries. NACA Tech. Note 2793.Google Scholar
Baba, N. & Miyata, H. 1987 Higher-order accurate difference solutions of vortex generation from a circular cylinder in an oscillatory flow. J. Comp Phys. 69, 362–396.Google Scholar
Bearman, P. W. & Fackrell, J. E. 1975 Calculation of two-dimensional and axisymmetrical bluff-body potential flow. J. Fluid Mech. 72, 229–241.Google Scholar
Cantwell, B. & Coles, D. 1983 An experimental study of entrainment and transport in the turbulent near-wake of a circular cylinder. J. Fluid Mech. 136, 321–374.Google Scholar
Celik, I., Patel, V. C. & Landweber, L. 1985 Calculation of the mean flow past circular cylinders by viscous-inviscid interaction. Trans ASME I: J. Fluids Engng 107, 218–223.Google Scholar
Fage, A. & Johansen, F. C. 1927 On the flow of air behind an inclined flat plate of infinite span.. Proc. R. Soc. Lond. A 116, 170–197.Google Scholar
Hurlbut, S. E., Spaulding, M. L. & White, F. M. 1982 Numerical solution for laminar two dimensional flow about a cylinder oscillating in a uniform stream. Trans. ASME I: J. Fluids Engng 104, 214–222.Google Scholar
Justesen, P. 1991 A numerical study of oscillating flow around a circular cylinder. J. Fluid Mech. 222, 157–196.Google Scholar
Keulegan, G. H. & Carpenter, L. H. 1958 Forces on cylinders and plates in an oscillating fluid. J. Res. Natl Bureau of Standards 60, 423–440.Google Scholar
Kiya, M. & Arie, M. 1977 An inviscid bluff-body wake model which includes the far-wake displacement effect. J. Fluid Mech. 81, 593–607.Google Scholar
Koterayama, W. 1984 Waves forces acting on a vertical circular cylinder with a constant forward velocity. Ocean Engng 11, 363–379.Google Scholar
Lecointe, Y. & Piquet, J. 1989 Flow structure in the wake of an oscillating cylinder. Trans. ASME I: J. Fluids Engng 111, 139–148.Google Scholar
Low, H. T., Chew, Y. T. & Tan, K. T. 1989 Fluid forces on a circular cylinder oscillating in line with a uniform flow. Ocean Engng 16, 307–318.Google Scholar
Matten, R. B. 1979 Loads on a cylinder in waves, currents and oscillating flow. PhD Thesis, Cambridge University Engineering Department.
Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics, 5th edn (revised). Macmillan.
Morison, J. R., O'Brien, M. P., Johnson, J. W. & Schaaf, S. A. 1950 The forces exerted by surface waves on piles. Pet. Trans. AIME 189, 149–157.Google Scholar
Mostafa, S. I. M. 1987 Numerical simulation of unsteady separated flows. PhD Thesis. Naval Postgraduate School, Monterey.
Parkinson, G. V. & Jandali, T. 1970 A wake-source model for bluff body potential flow. J. Fluid Mech. 40, 577–594.Google Scholar
Robertson, J. M. 1965 Hydrodynamics in Theory and Application. Prentice-Hall.
Roshko, A. 1954 A new hodograph for free-streamline theory. NACA Tech. Note 3168.Google Scholar
Sarpkaya, T. & Issacson, M. 1981 Mechanics of Wave Forces on Offshore Structures. Van Nostrand Reinhold.
Skomedal, N. G., Vada, T. & Sortland, B. 1989 Viscous forces on one and two circular cylinders in planar oscillatory flow. Appl. Ocean Res. 11, 114–134.Google Scholar
Smith, P. A. & Stansby, P. K. 1991 Viscous oscillatory flows around cylindrical bodies at low Keulegan-Carpenter numbers using the vortex method. J. Fluids Struct. 5, 339–361.Google Scholar
Tamura, T., Tsuboi, K. & Kuwahara, K. 1988 Numerical simulation of unsteady flow patterns around a vibrating cylinder. AIAA-88–0128.Google Scholar
Woods, L. C. 1955 Two-dimensional flow of a compressible fluid past given curved obstacles with infinite wakes. Proc. R. Soc. Lond. A227, 367–386.Google Scholar
Wu, T. Y. 1962 A wake model for free-streamline flow theory. J. Fluid Mech. 13, 161–181.Google Scholar
Verley, R. L. P. & Moe, G. 1979 The forces on a circular cylinder oscillating in a current. River and Harbour Laboratory, The Norwegian Institute of Technology, Rep. No. STF60 A79061.