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Introduction of RANS-CFD into the Initial Design Process

Stefan Krüger1, krueger@tuhh.de

Manuel Manzke2, manuel.manzke@tuhh.de Thomas Rung2, thomas.rung@tuhh.de

Hendrik Vorhölter 1, hendrik.vorhoelter@tuhh.de Hamburg University of Technology (TUHH), Hamburg/Germany

Abstract

The paper is devoted to the development of an efficient simulation process for an analysis of the hydrodynamic performance of vessels using RANS. Emphasis is given to the assessment of wake flows. Attention is given to robustness and process-efficiency aspects with respect to flow-physics and geometry modelling.

1. Motivation European shipyards are working in a competitive international environment. Due to the high labour costs, they have to compete with innovative and custom-made designs for specialised vessels like passenger ships or ferries. Custom-made designs are often adherent to elaborate design cycles. In order to meet the process timing, they rely on fast processes with featuring a deeper insight into the performance of the design already in the pre-contract phase. Accordingly, there is only a narrow time window to analyse and improve the design in greater detail. Model test are still crucial to the assessment of the hydrodynamic design. Such tests are necessary to verify the propulsion performance and to elucidate more sophisticated relevant aspects, e.g. pressure-pulse levels above the propeller - which are very important for the high comfort classes of passenger vessels. Due to the associated overhead, it is generally not possible to perform model tests before signing a contract. Moreover, intensive model testing of an optimised design is often not feasible due to the respective costs and time. Potential-flow methods are nowadays routinely used in industrial design projects to optimise the wave resistance preliminary to the model tests. Inviscid potential-flow methods can not be used for the optimisation of the wake, which is dominated by viscous effects. The quality of the wake field is governing for the pressure pulses induced by the propeller on the ship hull. The topic can be addressed by RANS-methods, which are traditionally deemed to be afflicted by a prohibitive effort, comparable of model tests. In order to reduce the effort of a RANS analysis, a process chain involving a ship-design system, semi-automatic grid generation as well as a RANS code was jointly developed between the institutes of Ship Design and Ship Safety (SSI) and Fluid Dynamics and Ship Theory (FDS) at the Hamburg University of Technology (TUHH). This process chain allows the analysis of a totally new design within a few hours and is applicable in the early design phase. 2. Initial design process The design process for the hull of a ship is traditionally governed by a sequence of different model tests (see figure 1, left side), viz. .

� The design specification, like desired speed and deadweight, lead to an initial hull design. The initial hull is afterwards tested in a towing tank

� If the resistance and propulsion tests are not successful, the design has to be revised and the model is re-manufactured.

� After successful propulsion tests, the wake field is measured. On the basis of this wake field a propeller is designed.

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� The new propeller together with the hull form is then analysed in a cavitation tunnel. If the limits for cavitation and pressure pulses are not kept the loop continues with a re-design of the propeller or even of the hull form. The global process is obviously time consuming and expensive.

Fig.1: Initial design process (left) and optimisation using CFD (right).

2.1 CFD in the early design Fig. XX (right) illustrates the optimisation loop using CFD methods. The optimisation loop is introduced into the initial design process subsequently to the hull form design and prior to the first model tests. Thus, CFD helps to push the optimisation of the design.

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The CFD-based optimisation consists of the following steps. Firstly, the bare-hull performance is analysed with a potential flow method, which is substantially faster than a RANS computation. Several design variants can be tested with respect to the wave resistance and provide a first glance at the flow field around the ship and the expected pressure distribution on the hull. During the next step, the optimised hull form is assessed with RANS methods. Again, the analysis provides not only the resistance and the nominal wake field but also further details of the flow field which might - for example - be used for the optimisation of the shape and the configuration of appendages. However, the efficiency of the employed RANS-process is significant for its applicability in an industrial process. The approach used at TUHH aims at this goal and is described in the following chapter. 3. RANS-CFD process chain The RANS process can be sub-divided into five consecutive steps (cf. figure 2). The initial step consists of the geometry preparation. At TUHH, this is done in the ship-design environment E4. The second step is the automatic generation of high-quality, hexahedral meshes, which utilises the automatic mesh generator HEXPRESS. This is followed by the set-up of the computational model and the actual computation. The final step is of course the analysis of the CFD results. If the CFD process is embedded in a design loop, as described above, this step is followed by geometry modifications in a goal-oriented iterative manner. During the initial design process, several geometry versions have to analysed in a short period of time. Moreover, geometry variations have to be included at short notice. Therefore, the principal focus of the RANS-application is on its robustness and the reduced time-to-response and -solution. In order to avoid errors, user interaction is minimised. To maintain reproducibility and comparability of design variants, the process is mostly automated. On intention, it is accepted, that some of the functionalities are thereby constrained. The five steps of the RANS-CFD process for the initial design used at TUHH are described by Figure 2.

Fig.2: RANS-CFD process chain.

3.1. Geometry preparation The geometry information extracted from a CAD-system can usually not directly be processed by a CFD-mesher. On the one hand, many details don't need to be considered by the CFD-investigation. On the other hand, additional geometry parts which are needed only for the CFD-investigation have to be included. An example for an additional geometry refers to a hub on the end of a shaft line. Additionally, any gaps of the wetted surface have to be closed prior to the meshing process. The internal geometry description in E4 is dedicated to rapid hull-form modifications and a rapid processing of hydrostatic and hydrodynamic computations. The geometry definition in E4 is not necessarily watertight, for instance the transom might be open. Moreover, the hull form provided by E4 is usually divided into a fore- and aft-body.

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In order to achieve a valid geometry description, two steps are performed in E4. Firstly, each part of the surface description is triangulated. Secondly, the various parts are combined in a single geometry. For usual single-screw and twin-screw hull forms, this is an automated process without user intervention. Appendage geometries or recesses, e.g. for manoeuvring devices, can be introduced into the model by the user. Therefore, a new module for E4 was developed which allows blending and transformation operations of triangulated geometry entities. Figure 3 shows the triangulated hull-form description of a fully appended twin-screw vessel including hull, shaft line, brackets and rudder.

Fig.3: Triangulation of a fully appended twin-screw vessel.

External boundaries have to be defined and located for the viscous CFD computation. The generation of the external domain is also performed inside E4. A standard boxed-shaped domain, with an extension based on the ship length, embedding the laterally centred ship model located on the waterline, can be generated automatically. For most applications, the free surface is represented by a symmetry plane. Optionally, the free surface obtained from potential-flow computations using the KELVIN software, which is integrated in E4, can also be used as a free-surface boundary of the domain. The domain displayed in figure 2 features such a deformed free surface, which is triangulated and blended with the hull geometry. The output of the E4-module is an STL-file. STL-files can be process by nearly any mesh generators. In order to be able to use the full potential of the HEXPRESS software, especially its functionality of resolving knuckles in the geometry by the mesh, the STL-description is expanded by a second file. This file assigns each facet to a certain face. The detection of the faces is also done in the respective E4-module. Figure 4 shows the edges between the different faces on the aft part of the twin-screw vessel.

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Fig.4: Connected (green) and unconnected (red) edges of the geometry.

The edges of each face are marked with lines. Green lines mark connected edges between two faces, whereas edges, which are not connected to any other part of the geometry are marked red. Thus, the user can easily identify errors and gaps in the geometry description. 3.2. Mesh generation The mesh generation is done with the automatic mesh generator HEXPRESS. The software combines the benefits of automatic mesh generation with high-quality hexahedral meshes. The user only needs to initialize the mesh generation and verify the outcome of the process. The initialisation is done by defining a small amount of parameters, like the parameter for the initial mesh and the maximum number of cell refinements. No complex blocking strategy has to be developed as it has to be done for the classical block-structured mesh generators. The disadvantages are that user has little influence on the mesh quality in detail, which is less important due to the generally satisfactory quality delivered by HEXPRESS. HEXPRESS generates a fully hexahedral mesh by subdividing an initial mesh, which was defined by the user. The possibility to generate fully hexahedral meshes together with the aspect, that HEXPRESS can reproduce edges of the geometry in the mesh, are the main advantages of HEXPRESS compared to other automated mesh generators like SnappyHexMesh or StarCCM+. The CPU-effort for the generation of a fully-appended ship-hull mesh including a viscous cell layer along the hull is about 15min for 1 Mio. cells on a standard PC with a 2.33GHz CPU and 12GB RAM.

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Fig.5: Snapshot of the mesh cells on the surface of the aft hull in HEXPRESS.

3.3 Set-up of CFD-model Most RANS-CFD-codes are universal and can be used for nearly any application. Therefore a lot of different discretisation schemes, transport equations, turbulence models and the like are implemented in the code. But for a standard analysis most off the set-up like the choice of turbulence model and descritisation scheme is fixed. Therefore, one can reduce the necessary input required by the user to the flow speed and a reference length, as all other input values are depending on these two numbers. For a ship analysis the ship length is usually used as reference length. At SSI a module for the ship design system E4 has been developed which uses the data of the ship already available in the system, like the ship length and the design speed. Thus, the user has only to define the model scale. The set-up for standard manoeuvres like drift or turning cycles can done by defining the drift angle and a turning rate. All other input values are computed automatically. For example are the coordinates of the rotation origin computed from the turning rate, the track speed and the longitudinal centre of gravity which is stored in the E4 ship model.

Fig.6: Snapshot of the E4-module for the RANS-CFD set-up

The result of the set-up module is the input file for the RANS-CFD solver. The present study refers to FreSCo software, which is an in-house development of TUHH, the Hamburg Ship Model Basin

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(HSVA) and MARIN. 3.4 Processing The processing of the RANS-CFD computation is done in parallel on a standard PC with two quadcore CPU with 2.33GHz and 12GB RAM. A computation for one half of the ship (symmetrical body) without computation of the free surface in the RANS-Code takes about 3h with a mesh of 600.000 cells. Usually the computations are performed in model scale in order to reduce the number of cells in the mesh and the computational effort. Thus, the results of the computation can directly be compared with towing tank measurements. 3.5 Post-processing The resistance of the body is a direct output of the RANS-CFD-solver. Visualisation of the flow field and the pressure field is done in ParaView. ParaView is an open-source visualisation toolkit based on the vtk-library. Section plots of the flow field as well as pressure distributions (cf. Fig. XX) are used as input for the form optimisation. 4. RANS-code FreSCo The Finite-Volume Navier-Stokes procedure FreSCo uses a segregated algorithm which is based on the strong conservation form of the momentum equation and employs a cell-centered, co-located storage arrangement for all transport properties. The procedure can be used in conjunction with structured-grid and unstructured-grid discretisations, based on arbitrary polyhedral cells including cells with hanging nodes. The implicit numerical approximation is second-order accurate in space and time. Integrals are approximated using the conventional mid-point rule. Diffusion terms are subsequently approximated using second-order central differences, whereas advective fluxes are approximated using high-order bounded (monotonic) schemes. The latter are applied in scalar form by means of a deferred correction approach. The odd-even decoupling problem of the cell-centered scheme is suppressed with a fourth-order artificial dissipation pressure term in the continuity equation. The solution is iterated to convergence using a pressure-correction scheme. Various turbulence-closure models are available with respect to statistical (RANS) approaches. Two-phase flows are addressed by interface-capturing methods based upon the Level-Set or Volume-of-Fluid (VOF) technique. To simulate cavitating flows, the VOF-method can be combined with a selection of mass-transfer models. Fully conservative interface-sharpening techniques are optionally available. Linear equations systems are solved by means of Krylov-subspace methods offered by the PETSC library. Since the date structure is generally unstructured, suitable preconditioned iterative sparse-matrix solvers for symmetric and non-symmetric systems (e.g. GMRES, BiCG, QMR, CGS, BiCGStab) can be employed. The algorithm is parallelised using a domain-decomposition technique based on a Single Program Multiple Data (SPMD) message-passing model, i.e. each process runs the same program on its own subset of data. Inter-processor communication employs the MPI communications protocol. Load balancing is achieved using the ParMETIS partitioning software. 4.1 Key requirements for Integration of FreSCo/RANS-CFD into the Initial Design Process The integration of FreSCo into the early design process requires that accurate results can be rapidly obtained. These two requirements are in generally contradictory, since accurate results require high-resolution (CPU-intensive) meshes. Thus it is crucial that the method reliably predicts the primary effects on the wake field even on coarse meshes. The accuracy of the predicted wake fields are mainly governed by a fair development of the boundary layer, including separation and transport of vortices created in the bilge region and the aft body. For

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an accurate prediction of the boundary layer with coarse meshes, wall-functions have to be used. Although their validity is confined to equilibrium boundary layers, they are still defensible for the major portion of the ship. More relevant aspects are the suppression of premature transition to turbulence due to irrotational strains in the stagnation-point regime and the ability to mimic the interaction between turbulence and curvature. Vortices's introduced at the bilge of a ship are difficult to capture with RANS-based methods using two-equation Boussinesq-viscosity turbulence closures. Simple RANS models often tend to introduce an unrealistic amount of diffusion through the eddy-viscosity. The present effort aims to bias this trend by means of a simple, curvature sensitive turbulence models and a vorticity confinement strategy, which tries to counter-act the viscous dissipation term in the vorticity transport equation. 4.2 Turbulence Modelling Amongst the many issues of engineering-turbulence modeling, the accurate predictive response to streamline curvature and non-inertial effects is perhaps the most crucial. Streamline curvature has a disproportionately large influence on both, the evolution of the shear stress and the turbulence energy. The majority of Boussinesq-viscosity turbulence-closures is derived for the prediction of weakly curved, plane shear flows. Accordingly, their predictive performance significantly deteriorates for 3D industrial flows. The latter is of significance for the predictive accuracy of wake simulations, since vortical flow features are most pronounced in this regime and are even more present for simulations with active propulsion. The predictive success for curved 3D flows hinges on both, an accurate prediction of the turbulence-production mechanism and an adequate representation of curvature-related convective transport of the stress anisotropy tensor. A non-linear, explicit algebraic stress model (EASM) Lübcke et al.(2003) offers an accurate representation of the curvature influences on the production mechanism and can thus close the gap between the standard low-cost Boussinesq-viscosity model (BVM) and the Reynolds-stress transport models, which are afflicted with a prohibitive computational surplus. The curvature influences are most dominantly seen in the linear term, thus a linear truncation seems to be defensible. The present study adopts the rationale of recently developed linear stress-strain relations (linearised explicit algebraic-stress models; LEA) by means of invariant methods and the physical realisability of the modeled Reynolds stresses Franke et al. (2005). The present k-w modeling framework Wilcox (1988) captures the distinct influences of strain-rate and rotation-rate invariants entering the stress-strain relation, viz.

122

32 21

1

,with 0.09 22

3

t

ckc

gg g

µµ

βνω ββ ηη

η

= =

− −

where k denotes the turbulent kinetic energy and ω the specific energy dissipation rate. The invariant iη coefficients read

2

1

1

11( )

km mk

km mk

km mk

S S

W W

S S

ηη

ηω

=

=

with kmS being strain-rate tensor and kmW the vorticity-rate tensor. The constants iβ are derived from

a pressure-strain rate model of energy re-distribution and assigned to the values of

1

2

3

0.46

0.775

0.375

βββ

= −= −= −

The coefficient g reads

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1.5P

gε

= +

P denoting the production of turbulence energy and ε the dissipation of turbulent energy. In order to additionally mimic the influence convective anisotropy transport, this promotes an attenuation of turbulence in convex curvature regions, a simple modification of the vorticity-rate entering the formulae is devised, i.e.

1002.31

100 100 1km mk km mk

km km

km mk km mk

S S W WW W

W W S S

+ = +

+ +

4.3 Vorticity Confinement The idea of vorticity confinement goes back to Steinhoff (1994), who introduced the concept. Basically a source term if is added to the momentum equation

( )iki i

i k

Du pf

Dt x xρ τ ρ∂ ∂= − + +

∂ ∂

The source term consists of the product between a scalar-valued velocity and a vector-valued reciprocal time scale is .

i if sε= − The time-scale is evaluated viz

i ijk j ks nε ω= with

, jj k k

j j

xn

x x

ηη ω ω

η η

∂∂

= =∂ ∂

∂ ∂

pointing towards the core of a vortical region and

jk kmj

m

u

xω ε

∂=

∂

being the vorticity vector. In the original work of Steinhoff, the velocity scale ε is kept constant, which can lead to inconsistent specific values for different applications. Moreover, constant velocity scales yield problems in areas featuring either large variations of vorticity (i.e. boundary layers) or numerical dissipation, e.g. due to large mesh variations. As the dissipation of the vorticity can be attributed to an enhanced level of eddy-viscosity in areas of large streamline curvatures (i.e. vortex cores), it is appropriate to couple ε to the turbulence velocity scale, viz. k

kε αλ= Furthermore, the confinement should not alter the boundary layer flow, thus a near-wall damping λ based on the wall-normal distance l is introduced

tanh500

klρλµ

=

which is close to zero in the boundary-layer region and approaches unity in the free stream. α is an user-prescribed confinement factor. 5. Examples This section outlines two illustrative examples. The first example demonstrates the influence of the

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applied vorticity confinement on the predictive performance of wake flows. Subsequently, an analysis of a complex geometry including appendages is discussed. 5.1 Influence of vorticity confinement on wake field of KVLCC2 To demonstrate the influence of vorticity confinement on wake-field predictions, the well-known KVLCC2 container ship is computed at model-scale Re-number (Re=5.085e6). The example included employs a symmetry plane representation of the free-surface, which is defensible due to the low Froude-number. Initial conditions refer to an approach flow turbulence intensity of 0.01. The approach level of the eddy viscosity ratio is assigned to 0.1. Experimental data is taken from Korea Research Institute of Ships & Ocean Engineering (KRISO) towing tank experiments Van et al. (1998a), Van et al. (1998b). Figure 7 depicts the axial velocity in propeller plane using the k-w standard turbulence model in comparison to the experimental results. The position of the velocity minimum in the centerplane is shifted towards the free surface in comparison to experimental results. Furthermore the hook shape in the wake field which is observed in the experimental results is hardly found in the simulation.

Fig.7: Comparison of measured (left) and computed (right) axial velocity using k-w standard

turbulence model in propeller plane of KVLCC2. Figure 8 illustrates the analogous result obtained from the LEA k-w turbulence model. As regards the hook shape, no improvement can be seen. However, the location of the velocity-minimum is in better agreement with experimental results.

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Fig.8: Comparison of measured (left) and computed (right) axial velocity using LEA k-w turbulence

model in propeller plane of KVLCC2. Figure 9 compares the predicted results using the LEA k-w model with (α = 1e-6) and without vorticity confinement. Due to the vorticity confinement the hook shape can be seen in the wake field and the predicted value of axial velocity in the symmetry plane is slightly higher.

Fig.9: Comparison of computed axial velocity using LEA k-w turbulence model with (left) and

without (right) vorticity confinement in propeller plane of KVLCC2. The comparison of experimental results and predictions obtained from the LEA k-w turbulence model with vorticity confinement is displayed in figure 10. The hook shape is still not fully captured. However, the figure indicates a remarkable improvement of the achievable accuracy in comparison to

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results obtained in conjunction with the standard k-w turbulence model and no vorticity confinement (cf. figure 7.

Fig.10: Comparison of measured (left) and computed (right) axial velocity using LEA k-w turbulence

model with vorticity confinement in propeller plane of KVLCC2. 5.2 Appendage analysis for a twin screw vessel The appendage design of a 200m twin screw vessel is analysed with the described process chain. The model is fully appended including shaft line with bossings, V-bracket and a rudder with rudder bulb. The hub in the end of the shaft line is elongated. Thus it overlaps with the rudder bulb. From the geometry definition in E4 a CFD-model is generated and the model is processed in FreSCo. The geometry model can be seen in figures 3 to 5. The computations are performed in model scale in order to allow the direct comparison with model tests. In this case the free surface is model fixed in the geometry and is generated by the potential flow solver Kelvin. The pre-processing for the RANS-CFD computation including geometry preparation, mesh generation and the set-up of the CFD-model takes about 1h. The processing is performed on a usual PC with two quad-core CPUs with 2.33GHz and 12GB RAM and takes about 3h. The size of the mesh is about 850000cells. The first step of the post-processing is to compare the resistance force of the measurement and the computation. For the presented computation the resistance was over predicted by about 1% of the measured resistance force. Hence, one can say that the resistance is fully captured as the difference is in the same scale as the accuracy of repetition of the model tests.

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Fig.11: Comparison of the measured (left) and computed nominal wake field (right)

In figure 11 measured and the computed nominal wake field are compared. The contour lines indicate the axial velocity, whereas the arrows show the velocity in the propeller plane. The main characteristics of the wake field are captured quit well. The major difference between the two is the thickness of the boundary layer, which is over predicted from the CFD. In this case the vorticity confinement technique was not used.

Fig.12: Pressure coefficient and velocity contour on the aft part of the hull

Figure 12 shows the pressure coefficient on the surface of the model together of with contour lines of the overall velocity. The pressured distribution especially on the appendages can be used for a redesign to achieve a better wake field quality. The contour lines of the total velocity show how the boundary layer develops along the hull. The extremely thick boundary layer at the symmetry plane is caused by flow separation at the lower part of the bulbous bow. To avoid this flow separation at the bulbous bow could also be an aim for an optimisation of the design. 6. Conclusions The key challenge for the use of viscous CFD during the early design phase is the rapid generation of reliably accurate results. In order to successfully meet these requirements, the whole process chain

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has been analysed and adjusted for wake-field computations. The geometry description entering the mesh generator is automatically derived from the geometry description in the ship design software (E4). The latter also includes the possibility to add appendages. The embedded geometry preparation facilitates a significant reduction of the associated effort. The computational mesh is created with an automatic mesh generator (HEXPRESS). High-quality hexahedral meshes are used which also substantially augment the robustness. In conclusion, target mesh sizes of the order of 1 Mio. control volumes can be generated within 15 minutes. Reliably accurate RANS results on - admittedly - coarse meshes are obtained, using appropriate turbulence models specifically dedicated to capture the primary effects of the wake field. Furthermore, vorticity confinement is applied to counter-act the enhanced dissipation of vortices on coarse meshes. The amount of data produced by a viscous flow simulation is rather large, thus all design-relevant post-processing of the results - including the data reduction to subsets - is generated automatically. Combining all above mentioned aspects, a process chain was developed that allows the use of RANS-CFD methods in the early design phase. An analysis for a fully-appended model can be performed in a few hours on a standard PC hardware (8 cores, 10GB RAM). Thus, the results of the RANS-CFD computation can be used for design optimisation. References FRANKE, M.; RUNG, T.; THIELE, F. (2005), Advanced Turbulence Modelling in Aerodynamic Flow Solvers. In: N. Kroll, J.K. Fassbender (eds.) MEGAFLOW - Numerical Flow Simulation for Aircraft Design, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Vol. 89, Springer Verlag pp. 225-240 LÜBBCKE, H.; RUNG, T.; THIELE, F. (2003), Prediction of the Spreading Mechanism of 3D Turbulent Wall Jets with Explicit Reynolds-Stress Closures, Journal of Heat and Fluid Flow, Vol. 24(4), pp. 434-443 STEINHOFF, J. (1994), Vorticity Confinement: A new technique for Computing Vortex Dominated Flows, Frontiers of Computational Fluid Dynamics, John Wiley and Sons, pp. 235-263 WILCOX, D.C. (1988), Re-assessment of the scale-determining equation for advanced turbulence model, AIAA Journal, Vol. 26, pp. 1414-1421 VAN, S. H.; KIM W. J.; KIM, D. H.; YIM, G. T.; LEE, C. J.; EOM, J. Y., (1998a), Flow measurement around a 300K VLCC model. Proceedings, Annual Spring Meeting, SNAK, Ulsan, Korea, pp. 185–188. VAN, S. H.; KIM, W. J.; YIM, G. T.; KIM, D. H.; LEE, C. J., (1998b), Experimental investigation of the flow characteristics around practical hull forms., Proceedings, 3rd Osaka Colloquium on Advanced CFD Applications to Ship Flow and Hull Form Design, Osaka, Japan.