Hydrodynamic forces on fixed submerged cylinders

Abstract

Wave loads on the cylindrical members of fixed offshore structures are generally calculated by using Morison’s Equation. The inertia force component of this equation is conventionally quoted in a form derived from theoretical calculations for a uniformly accelerating fluid. In this paper the correct form for the inertia force in a general fluid flow is derived from first principles by pressure integration and, independently, from earlier work, by energy arguments. It is shown that, for the thin cylinder limiting case, the transverse force on a circular cylinder is incorrectly given by the conventional approach, in that the product of transverse fluid velocity (in the direction of the required force) with the longitudinal velocity gradient should be added to the water particle acceleration, when computing the added-mass component of the force. Axial divergence, in other words, appears to play the role of a rate-of-change of added mass. It is shown that the mathematical origin of this extra term is the classical three-dimensional flow feature of a ‘zonal harmonic’, which produces a convective fluid acceleration but zero loading. A more elaborate formula is derived for non-circular cylinders, and the nature of point loads occurring at cylinder ends is also discussed.

Higher harmonic wave loads on a vertical cylinder in finite water depth

“…For circular cross-sections, the distributed force terms in Rainey's model (Eqn. (22) in Manners & Rainey (1992)) agree with F in the FNV model, given by (2.2). The only difference between the two load models is therefore the F ψ term.…”

Nonlinear Inertial Loading. Part I: Accelerations in Steep 2-D Water Waves

“…Rainey (1989) derived these terms using arguments based upon the conservation of energy coupled with the assumption that the position of the water surface is una!ected by the presence of the structure (i.e., it corresponds to the limiting case in which the cylinder is reduced to a line with hydrodynamic properties). In a subsequent paper, Manners & Rainey (1992) derived identical results using an independent method based on pressure integration. The advantage of this latter approach is that it provides some physical insight into the source of the axial divergence force, suggesting that it is related to the rate of change of added mass.…”

“…Much of this work was motivated by Lighthill (1979) in which he stated that there were additional nonlinear potential #ow loads which should be added to the standard Morison's inertia term. More recently, Rainey (1989Rainey ( , 1995a, Manners & Rainey (1992), Faltinsen et al (1995) and Newman (1996) have also tackled this problem. Detailed discussions of these papers will be left until Section 6.…”

“…In particular, an additional second-order force (often referred to as the axial divergence term) has been derived independently by Rainey (1989) and Faltinsen et al (1995). Furthermore, although the third-order loads predicted by Manners & Rainey (1992) appear substantially smaller than those derived by Faltinsen et al (1995), the latter solution includes the local disturbance of the wave"eld due to the presence of the cylinder, whereas the former was derived for a genuinely slender body in that the position of the water surface was una!ected by the structure. After correcting for this e!ect, Rainey (1995a) provides a uni"ed result.…”

A model for quick load analysis for monopile-type offshore wind turbine substructures

“…which according to Manners and Rainey, Manners and Rainey (1992), corrects for the assumption that the cylinder is slender in the vertical direction. Here the vertical particle velocity is denoted w and index "x" means that the variable is differentiated with respect to x.…”