A Numerical Approach to Assess Marine Fouling Tolerability on the Hull of Surface Vessels

Abstract

AbstractMarine fouling on the hull of surface vessels is a topic of increasing importance in the maritime field for its environmental and financial impacts. Recent research developments have introduced mathematical models dealing with the frictional resistance associated with fouling. Herein, an implementation of these models in a numerical code to predict the added resistance of ships due to biofouling and associated costs is presented. The code is designed to account for the singularity of each context based on at least one observation of the fouling condition. Through a hypothetical yet realistic scenario, it is shown that it enables proactive management by indicating when fouling is no longer tolerable from a financial standpoint. <def-list>Nomenclature<def-item><term>B</term><def>log-law intercept (=5.0)</def></def-item><def-item><term>CA</term><def>correlation allowance</def></def-item><def-item><term>CC</term><def>cleaning cost</def></def-item><def-item><term>CF</term><def>frictional resistance coefficient</def></def-item><def-item><term>Cf</term><def>local skin friction coefficient</def></def-item><def-item><term>Cfuel</term><def>cumulative added fuel cost</def></def-item><def-item><term>Cfuel</term><def>fuel price</def></def-item><def-item><term>CR</term><def>residuary resistance coefficient</def></def-item><def-item><term>CT</term><def>total resistance coefficient</def></def-item><def-item><term>CV</term><def>viscous resistance coefficient</def></def-item><def-item><term>FC</term><def>cumulative extra fuel consumption</def></def-item><def-item><term>Fn</term><def>Froude number</def></def-item><def-item><term>g</term><def>acceleration due to gravity</def></def-item><def-item><term>KF</term><def>cumulative added power</def></def-item><def-item><term>K</term><def>roughness height</def></def-item><def-item><term>Ks</term><def>sand roughness height</def></def-item><def-item><term>1 + K1</term><def>form factor</def></def-item><def-item><term>L</term><def>length of ship</def></def-item><def-item><term>PB</term><def>brake power or engine power</def></def-item><def-item><term>PE</term><def>effective power</def></def-item><def-item><term>Ra</term><def>centerline averaged roughness height</def></def-item><def-item><term>Rn</term><def>Reynolds number</def></def-item><def-item><term>RT</term><def>total resistance</def></def-item><def-item><term>Rt</term><def>maximum peak to trough roughness height</def></def-item><def-item><term>Rt50</term><def>maximum peak to trough roughness height over a length of 50 mm</def></def-item><def-item><term>S</term><def>wetted surface area</def></def-item><def-item><term>U</term><def>velocity</def></def-item><def-item><term>Ue</term><def>freestream velocity</def></def-item><def-item><term>U τ</term><def>friction velocity = <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mimetype="image" xlink:href="MTS51201e16.gif"/></def></def-item><def-item><term>T</term><def>threshold time</def></def-item><def-item><term>Tsea</term><def>time spent at sea</def></def-item><def-item><term>ΔU+</term><def>roughness function</def></def-item><def-item><term>δ</term><def>boundary layer thickness</def></def-item><def-item><term>ρ</term><def>density of fluid</def></def-item><def-item><term>κ</term><def>Von Karman constant (=0.41)</def></def-item><def-item><term>η</term><def>efficiency of the propulsion system</def></def-item><def-item><term>μ</term><def>dynamic viscosity</def></def-item><def-item><term>υ</term><def>kinematic viscosity</def></def-item><def-item><term>τ</term><def>shear stress</def></def-item></def-list><def-list>Subscripts<def-item><term>clean</term><def>clean, newly coated</def></def-item><def-item><term>r</term><def>rough</def></def-item><def-item><term>sm</term><def>smooth</def></def-item></def-list><def-list>Superscript<def-item><term>+</term><def>normalized variable</def></def-item></def-list><def-list>Abbreviations<def-item><term>ATTC</term><def>American Towing Tank Conference</def></def-item><def-item><term>BMT</term><def>British Maritime Technology</def></def-item><def-item><term>IFO</term><def>intermediate fuel oil</def></def-item><def-item><term>IMO</term><def>International Maritime Organization</def></def-item><def-item><term>IPPIC</term><def>International Paint and Printing Ink Council</def></def-item><def-item><term>ITTC</term><def>International Towing Tank Conference</def></def-item><def-item><term>MEPC</term><def>Marine Environment Protection Committee</def></def-item><def-item><term>NSTM</term><def>Naval Ships' Technical Manual</def></def-item><def-item><term>SFOC</term><def>specific fuel oil consumption of engine</def></def-item></def-list>