Numerical hull resistance calculation of a catamarán using OpenFOAM

Resumen Simulación numérica de la resistencia al avance de un catamarán usando OpenFOAM Date Received: February 24th 2017 Fecha de recepción: Febrero 24 de 2017 Date Accepted: March 10th 2017 Fecha de aceptación: Marzo 10 de 2017 Numerical hull resistance calculation of a catamarán using OpenFOAM 1 Escuela Superior Politécnica del Litoral. Guayaquil, Ecuador. Email: dshurtad@espol.edu.ec 2 Escuela Superior Politécnica del Litoral. Guayaquil, Ecuador. Email: rparedes@espol.edu.ec Ship Science & Technology Vol. 11 n.° 21 (29-39) July 2017 Cartagena (Colombia) DOI: 10.25043/19098642.150

Th e resistance of a ship at a given speed is the force required to tow the ship at that speed in calm water, assuming no interference from the towing ship [3].Th e ship must provide the minimum shaft horsepower to cruise at required velocity.
Ship resistance estimation is a complex task.It can be broken down into frictional and residual components.In addition, there is an additional component in the case of catamarans, such as the interference between the demi-hulls.Th ere are three diff erent methods to predict ship resistance: empirical methods, model testing and numerical simulations.
In the last years, numerical simulations using CFD have become a third alternative used in the industry.Th e CFD solution is a numerical method to solve the nonlinear diff erential equations governing the fl uid fl ow.However, it cannot be used as a black box because it can produce spurious results if not set correctly.It is required to perform a verifi cation and validation procedure, usually using experimental data.
In this work, numerical simulations were performed to predict total resistance of a catamaran and results were validated using experimental data obtained by Chávez and Lucín [1].OpenFOAM is used to predict the catamaran resistance.It was chosen because of its customization options, online training and support, and it is open source.
Th e "Cormorant Evolution" Catamaran was built in Ecuador in 2011 by "Astilleros y Marina BOTTO CIA.LTDA", and operates through "Cormorant Cruise" in Galapagos Islands [4].It is a 32.5 [m] length fi berglass touristic vessel; with a "V" middle section, a bulbous bow, separation of 9.11[m] between the centerlines of hulls and a design velocity of 5.14 meters per second (10 knots).Subsequently a 2 [m] length model was built using Cormorant Evolution hull-shape, to measure experimental resistance in the lake of "Escuela Superior Politécnica del Litoral" (ESPOL) [1].Th e scale factor was λ=16.25.Th e experiment velocity range of the model was from 1.05 to 1.45 meter per second.Table 1 shows the main characteristics of the catamaran at two load conditions.
Open Source Field Operation and Manipulation (OpenFOAM) is a free source code with C++ programing language.Th is code creates executable

Abbreviations Introduction
Geometry and test conditions scripts, called applications that are divided in two categories: solvers developed for specific problems in continuum mechanics, and utilities developed to manipulate data.Fig. 2 shows the workflow of OpenFOAM.

Computational method
There are three physical laws that govern a fluid flow: Conservation of Mass, Conservation of momentum, and Newton's Second Law.However, these equations cannot be solved analytically for all types of problems.
One alternative is to solve them numerically using Computational Fluid Dynamics (CFD  For marine applications, two solvers can be used for multiphase fl ows, interFoam and interDyFoam.In this thesis, the InterFoam solver is applied because only ship resistances are measured in experiments.InterFoam is a solver for two incompressible, isothermal immiscible fl uids using a volume of fl uid phase-fraction based interface capturing approach [8].Th e computational domain includes fresh water and atmosphere.y + is the non dimensional distance and OpenFOAM is a post processing tool applied to near-wall cells of all wall patches.Th e value obtained by y + can describe the places where the mesh has to have a greater number of cells.y + is defi ned by: Where u * is the frictional velocity at the nearest wall, y is the distance to the nearest wall and v is the local kinematic viscosity of the fl uid.

3D Generation model
Th e 3D surface model was generated with the body and profi le plan in the Computer Aided Design (CAD) software Rhinoceros 3D [5] and positioned after the perpendicular line at the origin axes before exporting as a STL fi le to import into the CFD code, OpenFOAM.Fig. 3 shows the 3D Rhinoceros scaled demi-hull model.

Domain, grids and boundary conditions
Th e computational domain was built as a rectangular block around the hull (demi and twin hulls) in deep water; Fig. 4 shows the principal dimensions in meters.

Verifi cation and validation
To identify the mesh density needed for the Catamaran cases a mesh convergence study was perform.Th e domain was divided into six blocks with diff erent mesh densities.Table 2 shows the number of cells for each mesh.
To visualize the convergence of the simulations, Fig. 5 shows the force time history (4,000 (4) Results  3 shows the average of the last fi ve hundred values for the resistance of each mesh and its error when compared with an experimental value of R t exp =1.79 [N].
Th e errors bet ween meshes 2 and 3 are closer.But, analyzing the standard deviation, Mesh 2 has less variation of resistance in the analyzed steps.Mesh 2 was selected to set up the other simulations.Fig. 6 represent the mesh 2 confi guration around the hull.
As a post-processing tool, y + , was calculated to verify the mesh quality near the hull.A value of y + ≤100 is acceptable for the case of the catamaran.Fig. 7 shows the wall y + parameter for the submerged hull.
Bow, Stern and central keel are zones that required a grater mesh density.
Fig. 14 shows the pressure distribution the hull for Fn=0.34 (v=1.45 m/s).Th e labels of dynamic pressure was setting to capture as blue ones the zones with negative pressure and red ones the zones with positive pressure.For twin hulls, the pressure in the inner side of the hull is slightly greater than the pressure on the outside of the hull; this is due to the interference caused by the other hull.
Interference Th e catamaran interference was estimated following the expression [1]: Where: R W is the demi hull interference in Newton R T CAT is the total resistance of twin hulls in Newton R T is the total resistance of demi hull in Newton Th e interference factor obtained by numerical simulations is linear contrasting with the experimental interference published by Chávez and Lucín [1].Th e positive interference corresponds to increased interference (unfavorable) and the negative values to decrease (favorable).

Wave pattern
Figs. 17 to 19 shows the wave pattern for diff erent Froude numbers in Full load condition.
Before starting the Catamaran numerical resistance, several tutorials were carried out using the OpenFOAM user manual [6].Th ese tutorials were of great help to understand the capabilities and limitations of the software.Cavity was the fi rst made tutorial, for laminar and incompressible fl ows.Th e user manual gives an overview of the workfl ow of OpenFOAM: Pre-processing, solution and Post-processing.ParaView is a post-processing tool; the user manual also gives an introduction of its operation.Th is was an important step for understanding OpenFOAM and the principles of fl uid analysis.
A catamaran mesh convergence study was developed fi rst, with 3 types of mesh for a demi hull at Fn=0.The interference component between the twin hulls was estimated for Full and light Load conditions for Fn between 0.24 and 0.34.But these results were not those expected, because the curves of interference did not display the same trend.Also, the interference factor was calculated using the Maxsurf data and even though it was not very close, the Maxsurf interference had the same trend compared to numerical data.
These variations between experimental results and numerical simulations may be due to external factors, that can not be controlled or measured, such as: wind, water temperature, interference between the method of drag, towing velocity uncertainly, differences between the model and the catamaran, and range of work of Data Card available in our college.

Fig. 1 .
Fig. 1.Experimental test at ESPOL Lake Ship Science & Technology -Vol.11 -n.°21 -(29-39) July 2017 -Cartagena (Colombia) Numerical hull resistance calculation of a catamarán using OpenFOAM Th e following assumptions about the numerical model to be implemented are considered: i. Steady, turbulent and three-dimensional fl ow.ii.Single-phase fl ow.iii.Uniform velocity.iv.Constant air and water properties.

Fig. 5 .
Fig. 5.Total Resistance along the setting time of convergence for different mesh densities

Fig. 12 .
Fig. 12.Total resistance for twin hull in light condition

Fig. 14 .
Fig. 14.Pressure around the bulbous for twin hull

Figs. 15
Figs. 15 and 16 shows the interference factor for original hull separation at Light and Full load conditions.

Fig
Fig. 15.Interference for light condition

Ship
Fig. 16.Interference for load condition

Fig. 17 .
Fig. 17.Wave pattern at Fn=0.24 2453.Mesh 2, with 1 million of cells, was chosen to the simulation because had the lowest error and standard deviation at R texp =1.79 [N], error=5% and Sta.Dev.=0.34 [N].Due the extensive time of resolution, the interDyMFOAM solver was not taken into consideration in the Catamaran hull.Two load conditions were Conclusions Ship Science & Technology -Vol.11 -n.°21 -(29-39) July 2017 -Cartagena (Colombia) Hurtado, ParedesNumerical simulations using OpenFOAM are a feasible method for predicting the resistance of the Cormorant Evolution catamaran, despite the difference between experimental data and numerical simulation resistance.However, numerical results are close to statistical methods, such as Holtrop and Molland, estimated with Maxsurf Resistance software.

Table 3 .
Catamaran scale model dimensions Ship Science & Technology -Vol.11 -n.°21 -(29-39) July 2017 -Cartagena (Colombia) Numerical hull resistance calculation of a catamarán using OpenFOAM viscous.Fig. 8 shows Pressure and Viscous force components for the case of demi-hull in Light Condition at a velocity of V=1.05 [m/s].Th e experimental resistance is 1.79 [N] at Fn=0.2453.Total resistance was obtained by adding pressure and viscous forces.

Table 4 .
OpenFoam Resistance data for demi hull in light condition

Table 7 .
OpenFoam resistance data for twin hull in load condition