Keulegan-Carpenter Number
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Keulegan%E2%80%93Carpenter Number
Oseberg A - Waves I.jpg
Oseberg A - Waves II.jpg
The Keulegan-Carpenter number is important for the computation of the wave forces on offshore platforms.

In fluid dynamics, the Keulegan-Carpenter number, also called the period number, is a dimensionless quantity describing the relative importance of the drag forces over inertia forces for bluff objects in an oscillatory fluid flow. Or similarly, for objects that oscillate in a fluid at rest. For small Keulegan-Carpenter number inertia dominates, while for large numbers the (turbulence) drag forces are important.

The Keulegan-Carpenter number KC is defined as:[1]

where:

  • V is the amplitude of the flow velocity oscillation (or the amplitude of the object's velocity, in case of an oscillating object),
  • T is the period of the oscillation, and
  • L is a characteristic length scale of the object, for instance the diameter for a cylinder under wave loading.

The Keulegan-Carpenter number is named after Garbis H. Keulegan (1890-1989) and Lloyd H. Carpenter.

A closely related parameter, also often used for sediment transport under water waves, is the displacement parameter ?:[1]

with A the excursion amplitude of fluid particles in oscillatory flow and L a characteristic diameter of the sediment material. For sinusoidal motion of the fluid, A is related to V and T as A = VT/(2?), and:

The Keulegan-Carpenter number can be directly related to the Navier-Stokes equations, by looking at characteristic scales for the acceleration terms:

  • convective acceleration:
  • local acceleration:

Dividing these two acceleration scales gives the Keulegan-Carpenter number.

A somewhat similar parameter is the Strouhal number, in form equal to the reciprocal of the Keulegan-Carpenter number. The Strouhal number gives the vortex shedding frequency resulting from placing an object in a steady flow, so it describes the flow unsteadiness as a result of an instability of the flow downstream of the object. Conversely, the Keulegan-Carpenter number is related to the oscillation frequency of an unsteady flow into which the object is placed.

See also

Notes

  1. ^ a b Dean & Dalrymple (1991), p. 232.

References

  • Keulegan, G. H.; Carpenter, L. H. (1958), "Forces on cylinders and plates in an oscillating fluid", Journal of Research of the National Bureau of Standards, 60 (5): 423-440, doi:10.6028/jres.060.043
  • Dean, R.G.; Dalrymple, R.A. (1991), Water wave mechanics for engineers and scientists, Advanced Series on Ocean Engineering, 2, World Scientific, Singapore, ISBN 978-981-02-0420-4

  This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

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