The roll damping assessment via decay model testing (new ideas about an old subject)

Abstract

The methodology to obtain the non-linear roll damping from decay tests is very old. It has been proposed by Froude in the 19th century and used from then on. Behind it there is a quadratic model θ θ ⎡ ⎤ ⎣ ⎦ for the damping and a subsequent equivalent linearization. Probably all model basin in the world follows this approach to assess the damping from a decay test. This is well documented and so is the methods to get the p 1 -p 2 coefficients. This is very general in the sense that in principle, it could be applied to any kind of hull. However, it has become clear that for hull with a flat bottom such as a very large crude carrier (VLCC), this approach may lead to confusing results such as negative p 2 . Faced with this, the work presents a completely new idea. Avoiding the polynomial approximation, the basic attitude is to devise two regions from the decaying test response. The first, called the large amplitude response region yields a larger damping, probably due to the large bilge keel vortices that are attracted to the hull flat bottom. The second is the small amplitude response region where the vortices are not attracted to the bottom but travels approximately 45 º sidewise. These observations has led to a new approach called the bi-linear approach as discussed in the work after analyzing several (many) model test results. In fact, a new modified bi-linear approach is ultimately proposed after the understanding of a transition region instead of a transition angle.

Verification and validation of numerical modelling of DTMB 5415 roll decay

“…It can be further noted that 24.50, 19.58 and 13.50 deg decay curves converge in ten cycles in amplitudes lower than 5.0 deg. This behaviour of high damping at large roll amplitudes and small damping at small angles, has been indicated by Fernandes & Oliveira (2009) and suggesting possible different damping formulations for small and large angles.…”

An overview of the prediction methods for roll damping of ships

“…The group at the Federal University of Rio de Janerio and Lab Ocean (Fernandes and Oliveira, 2009) has recently made some unique observations on roll damping stating that it actually decreases for large angles.…”

The Nonlinear Roll Damping of a FPSO Hull

“…It is important to understand why the damping stops increasing (saturation). In fact, Oliveira and Fernandes [14] and Femandes and Oliviera [15] have proposed a methodology to deal numerically with this new data set. Modifying the bilinear methodology, which identifies two plateaus (see upper match of Fig.…”

“…Hyperbolical functions also have been used in other ship hydrodynamic applications (see Doctors and Sharma [20]). The 15 Froude procedure (quadratic regression) applied to odology (linear adjustment for a small-angle decay test) com-the FPSO decay data set; this kind of fitting seems better than pared with grouped data the more used (Faltinsen) approach Damping Evoludon Fig. 16 Hyperbolical tangent behavior as a function of a parameter; as the parameter increases, the function better approximates to a step function slope of the transition is controlled with the introduction of a new parameter a as shown in Fig.…”