Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Short-term Prediction of Nonlinear Added Resistance in Head Sea withProbability Density Function Method
Sahil Jawa1 Munehiko Minoura1 and Yu Idomoto2
1Department of Naval Architecture and Ocean Engineering, Osaka University, Osaka, Japan
2Imabari Shipbuilding Co. Ltd.

been treated by spectral analysis using added resistance transfer function
and wave spectrum that corresponds to statistical values in short term.
Meaning using the estimation of frequency response transfer function ofadded resistance in regular waves, the total amount is predicted by the
moment of response spectra criterion for calculating added resistance inshort-term sea conditions. Most of the studies focused on calculating theadded resistance transfer function accurately in regular waves. Also,
potential-based numerical methods are applied to predict the addedresistance more accurately. Seo et al. (2014) predict the added resistanceusing potential-based methods, and Lee et al. (2016) investigated theadded resistance using model tests. However, due to its limitations whichmake it difficult in considering the nonlinearity and viscosity effects.
However, all these approaches and methods are incomplete because theconcept of estimation of added resistance transfer function does notinclude the effect of the sea environment and does not reflect the wavebody interactions which is a crucial aspect of considering non-linearhydrodynamic effects.

ABSTRACT
A probabilistic method to estimate non-linearities of added resistancewith respect to wave height in short-term sea conditions is proposedusing the joint probability distribution of wave height and period andnon-linear added resistance response in the frequency region which isobtained by CFD numerical simulations for KCS hull type. The nonlinearity with respect to wave height is empirically expressed as a"correction coefficient" for linear calculations using CFD simulations
and correction is added to the theoretical linear calculation result. The
present systematic study demonstrates that the numerical results have areasonable validation with the linear-based methods and emphasizes thenon-linearity in the prediction of the added resistance with the varying
wave height in the irregular waves.

KEYWORDS:

Added resistance, regular waves, irregular waves,linear and nonlinear, CFD, KCS, short-term sea predictions

It is said that the increase in wave resistance is roughly proportional to
the square of the wave height, but there is a slight difference between thetheoretical value and the measured value. This is due to the non-linearityof the fluid near the ship hull. So, CFD tools are now increasingly applied
used to predict added resistance especially to account for their nonlinearities. For instance, it has been examined through experimental
studies that the added resistance transfer function is dependent on thewave steepness of regular waves and shows non-linearity with respect towave height. Therefore, a direct time-averaged estimation of added
resistance in irregular waves usually does not agree with the mean valueof the frequency domain traditional method Although direct estimation
can be done but the limitations of the basin facility and limited
computation capacity, and high computational costs are required tohandle various wave patterns that occur in irregular waves. Considering
the high computational resources and costs, it is not realistic to directly
calculate the increase in resistance in waves in a time series ofcomplicated sea conditions such as real sea conditions. Lang, X. et al(2020) also tried to propose a wave height correction factor in theINTRODUCTION
There is a growing demand for a highly accurate evaluation of the actualsea performance of ships from the viewpoint of the operational economy
and environmental protection. Recently, Energy Efficiency Design
Index (EEDI) regulations for the powering performance of commercial
ships have made it impossible to operate ships that do not meet specificstandards. It is more important to estimate ship propulsion performanceaccurately in actual sea conditions. When a ship travels in waves, thedrag on the ship increases by 15-30% compared to when it travels incalm water. One of the factors that affect ship performance in the actualseas is an increase in resistance during waves and it greatly affects theship’s performance in terms of sustainable service speed and fuelconsumption in realistic sea conditions. This is because waves are
generated by the ship's hull oscillating and reflecting incident waves, andthis increase in resistance is called the added resistance in waves.
Traditionally, calculation of added resistance in actual sea conditions has3392