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Experimental and Numerical Investigations on Flow Characteristics of
the KVLCC2 at 30° Drift Angle
Moustafa Abdel-Maksoud1, Volker Müller1, Tao Xing2, Serge Toxopeus3, Frederick Stern4, *Kristian Petterson5,
Magnus Tormalm5, Sungeun Kim6, Shawn Aram6, Uwe Gietz1, Patrick Schiller1, Thomas Rung1
1 Hamburg University of Technology, Germany, 2 University of Idaho, USA, 3 MARIN, Netherlands, 4 University of Iowa, USA,
5 Swedish Defence Research Agency (FOI), Sweden, 6 NSWCCD West Bethesda, USA.
Investigations of flow characteristics around ship hulls at large drift angle are very important for understanding the
motion behavior of ships during maneuvers. At large drift angles, the flow is dominated by strong vortical structures
and complex three-dimensional separations. An accurate prediction of these flow structures is still a challenge for
modern computational fluid dynamics (CFD) solvers. Hull forms with high block coefficients are blunt and have strong
curvatures, which leads to large area flow separations over smooth surfaces. These areas are sensitive to the relative
angle between the flow and the ship motion direction. The paper is concerned with a collaborative computational study
of the flow behavior around a double model of KVLCC2 at 30 degrees drift angle and Fr=0 condition, including
analysis of numerical methods, turbulence modeling and grid resolution, and their effects on the mean flow and
separation onset as well as formation of the vortical structures. This research is an outcome of a multi-year
collaboration of five research partners from four countries. The overall approach adopted for the present study
combines the advantages of CFD and EFD with the ultimate goal of capturing the salient details of the flow around
the bluff hull form. The experiments were performed at the low - speed wind tunnel of the Hamburg University of
Technology (TUHH). The main features of the global and local flow were captured in the experimental study. To
determine the global flow characteristics, two different flow visualization techniques were used. The first one is a smoke
test, which allows the visualization of vortex structures in vicinity of the ship model. The second test is a classic oil film
method, which yields the direction of the limiting wall streamlines on the surface of the model. The analysis of the
experimental results helped identify the separation zones on the ship model. To resolve the local flow-fields, LDA and
PIV measurements were carried out in a selected number of measuring sections. Subsequently, the EFD and CFD
results for the global and local flow structures were compared and analyzed. The numerical simulations were carried
out by 5 institutions: Iowa Institute of Hydraulic Research of the University of Iowa (IIHR), USA, Maritime Research
Institute Netherlands (MARIN), The Netherlands, Hamburg University of Technology (TUHH), Germany, Naval
Surface Warfare Center, Carderock Division (NSWCCD) West Bethesda, USA and Swedish Defense Research Agency
(FOI), Sweden. For the comparison with the experimental results, seven submissions of steady and unsteady CFD
results are included in the present study. The participating codes include CFDShip-Iowa, ReFRESCO, FreSCo+, Edge,
OpenFOAM (FOI) and NavyFoam. The size of the computational grids varies between 11 and 202 million control
volumes or nodes. The influence of turbulence modeling on the predicted flow is studied by a wide variety of models
such as isotropic eddy viscosity models of k-family, Explicit Algebraic Reynolds Stress Model (EARSM), hybrid
RANS-LES (DES), and LES. Despite notable differences in the grid resolutions, numerical methods, and turbulence
models, the global features of the flow are closely captured by the computations. Noticeable differences among the
computations are found in the details of the local flow such as the vortex strength and the location and extent of the
flow separations.
KEY WORDS: KVLCC2, Verification and Validation,
Turbulence models.
INTRODUCTION Investigations of flow characteristics around ship hulls at high
drift angles are very important for understanding the motion
behavior of ships during maneuvers. At high drift angles, the flow
is strongly dominated by vortical structures and large separation
areas. An accurate computation of these flow structures is still a
challenge for advanced computational fluid dynamics (CFD)
solvers. Hull forms with high block coefficients are blunt and
have a smooth surface, which leads to large area flow separation.
This area is sensitive to the relative angle between the flow and
the ship motion direction.
The viscous flow on ship hulls at 0° drift angle has been
extensively investigated in the last two decades. At the CFD
Workshop Gothenburg 2010 [18], various research groups
studied the flow on the tanker hull form KVLCC2 with large
block coefficient CB = 0.81 at calm water straight-ahead condition
with Fr = 0.142. Special attention was given to the wake field and
the flow structure in the stern region, especially 3D separation at
the stern, which was characterized by 2 co-rotating axial vortices
with hook-shaped axial-velocity contours in the nominal wake
plane (symmetric with respect to center plane).
The results presented by Bhushan et al. [2] show that when using
sufficiently fine grids, both URANS- and DES-based numerical
methods are able to provide good predictions of the mean flow on
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 2
KVLCC2. Compared with experimental wind-tunnel data,
differences can be seen in vortex strength and the turbulence
variables. According to the presented results in Bhushan et al. [2],
it can be concluded that anisotropic URANS models deliver more
accurate results than the isotropic models for the prediction of
onset and formation of vortical structures, but are too dissipative
even for fine grids. Hybrid RANS/LES models are promising in
providing the details of the flow topology, but show modeled
stress reduction and grid-induced separation in the boundary layer
issues for bluff bodies.
The calm water static and dynamic maneuvering conditions of
KVLCC2 were the topics of study at the Maneuvering Simulation
Workshops SIMMAN 2008 [32] and SIMMAN 2014 [33]. At the
2014 workshop, the X- and Y-force and the yaw moment acting
on the ship model with rudder at a static drift angle β = 12 degrees
and a rudder angle δ = 0 degrees were compared with
experimental data D. The comparison of the mean errors E for
surge force (X) are relatively high at about 44.39%D, and for
sway force (Y) and yaw moment (N) are relatively small at about
3.43 and 2.09%D, respectively.
Vortical and turbulent structures for KVLCC2 (Fr = 0) at β = 0,
12 and 30 degrees were investigated using DES and URANS for
KVLCC2 by Xing et al. [45]. One shear layer, one Karman-like
Vortex shedding and three helical mode instabilities were
identified. The After-Body Side Vortex, Fore-Body Side Vortex,
and After-Body Bilge Vortex exhibit all characteristics for helical
instability. For analyzing the helical instability in the wake of the
vortex, the Strouhal number, based on the ship’s length or the
distance along the vortex core, was considered. The turbulent
kinetic energy (TKE) peaks near the separation point at the bow
and on the vortex core of all vortices. For the After-Body Side
Vortex, TKE reaches the local maximum right after the helical
instability and intensifies along the vortex core further
downstream. In addition to the three steady vortices previously
identified, the simulations at β = 12 and 30 degree show unsteady
Aft-Body Hairpin and After-Body Side Vortices.
The objective of the present study is to verify and validate the
CFD for KVLCC2 at the β = 30 degree condition, which includes
the analysis of numerical methods, turbulence modeling and grid
resolution, mean flow and onset as well as formation of vortex
structures. This research is a collaborative of five research
partners from Germany, Netherlands, Sweden and USA. The
present paper documents the CFD results for KVLCC2 in deep
water without consideration of the free surface effect. The
experiments are performed at TUHH’s low-speed wind tunnel
and the CFD studies are carried out at 5 institutions with different
numerical methods, turbulence models and grid resolutions. The
CFD and EFD studies are consolidated such that the global flow
visualization in CFD complements EFD for identifying the
vortical structures; the EFD provides global and local
measurements for CFD validation; and once validated, the CFD
then fills in the sparse EFD, thus enabling detailed diagnostics of
the flow field.
As a successful validation requires precise planning of
experimental investigations, the published CFD results by Xing
et al. [45] using the CFDShip-Iowa code are evaluated to identify
the main flow characteristics and to localize the position of the
each vortex. After analyzing the CFD data, the experimental
setup is designed and the locations of the measurement planes are
determined. The experiments are designed to capture the global
and the local flow properties. In order to determine the global
flow characteristics, two different flow visualization experiments
are carried out. The first one is a smoke test, which visualizes
vortex structures in the flow field in the region close to the ship
model. The second test is a classic oil film method, which yields
the direction of the wall streamlines on the surface of the model.
The analysis of the experimental results provides the separation
zones on the ship model. To determine the local flow properties,
Laser Doppler Anemometry (LDA) and Particle Image
Velocimetry (PIV) measurements are carried out in the
previously defined measuring planes. Subsequently, the EFD and
CFD results for the global and local flow structures are compared
and analyzed.
The present study includes a summary of an experimental
investigation for the ship hull KVLCC2 at 30 degree angle of
attack in the TUHH wind tunnel and a comparison between the
measured and CFD results. The numerical calculations are carried
out at Iowa Institute of Hydraulic Research (IIHR) of the
University of Iowa, USA, Maritime Research Institute
Netherlands (MARIN), The Netherlands, Hamburg University of
Technology (TUHH), Germany, Naval Surface Warfare Center,
Carderock Division (NSWCCD), USA and Swedish Defence
Research Agency (FOI), Sweden.
OVERVIEW OF EXPERIMENTAL VALIDATION
VARIABLES AND CFD SIMULATIONS The experimental investigations focus on the global and local
flow structures on the ship hull KVLCC2 at 30 degree drift angle.
The global flow structure is captured by applying two flow
visualization tests.
Table 1: Overview of performed wind tunnel experiments at
TUHH.
Experiment
Wind
tunnel
velocity
Measured variables / aim
PIV 27 m/s Velocity components, Ux, Uy, Uz
Vorticity component ωx
LDA 27 m/s
Tangential velocity
component Ut, and its turbulence
degree TUt.
Smoke test 12 m/s Vortex visualizations
oil film test 27 m/s Limiting streamline visualization
The local flow structure is obtained from velocity measurements
at pre-defined cross sections. Flow velocities are measured
mainly by PIV technique. Additional LDA measurements are
conducted to get a reliable resolution close to the hull. An
overview of the available model test data is given in Table 1.
The numerical simulations are carried out by 5 institutions. For
the comparison with the experimental results, 7 submissions are
included in the present study. The codes involved are CFDShip-
Iowa (IIHR), ReFRESCO (MARIN), FreSCo+ (TUHH), Edge
(FOI), OpenFOAM (FOI) and NavyFOAM (NSWCCD). The
finest grid of each submission varies between 11 and 77 million
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 3
control volumes. The influence of the turbulence on the flow is
investigated with a wide variety of models such as Explicit
Algebraic Reynolds Stress Model (EARSM), Detached Eddy
Simulation (DES), k-ω- SST (1994 and 2003 versions), EARSM
in combination with Hellsten k-ω, Large Eddy Simulation (LES),
RANS-LES and Mixed Model (MM). Computations are carried
out either as steady or unsteady condition. An overview of the
submissions is given in Table 3.
EXPERIMENTAL INVESTIGATION The experimental investigation for the very large crude oil carrier
hull form (KVLCC2) is carried out at the TUHH’s Institute for
Fluid Dynamics and Ship Theory (FDS). A double model of the
KVLCC2 is installed in the low speed wind tunnel. The free
stream velocity is fixed at 27 m/s. Dimensions of the model are:
LOA = 1.6m, Lpp = 1.535m, B = 0.279m, 2 x T = 0.206m, and
the corresponding Reynolds numbers based on the model length
is 2.74 × 106.
The measurements consist of smoke tests for the flow
visualization as well as the spatial distributions of the velocity
components at predefined planes in the bow, midship, stern
regions and behind the model. The measurements focus on the
longitudinal vortices formed on the hull and in the near-wake
region.
Wind Tunnel The wind tunnel measurements are performed using the 5.5m
long open test section with a cross-sectional area of 6m2. The
degree of the free stream turbulence is less than 0.3%. The test
section allows manual and optical access from the top and the two
lateral sides. Positioning the intrusive and non-intrusive
measurement sensors is supported by a multiple-axes traversing
system mounted to the lateral sides of the section. This two-
component traverse system is used to move the complete PIV or
LDA system for measuring the flow velocity at various planes
and positions.
Ship Model The MOERI tanker KVLCC2 without any appendages is
considered in the CFD and experimental investigations [32]. A
double-body model of the underwater hull of KVLCC2 is used
for the experimental investigations in the wind tunnel. Compared
with the original draft of the ship, the draft of the investigated
model is slightly increased in order to avoid a strong discontinuity
of the hull near the forward perpendicular. The CAD-data of the
hull are mirrored about the waterline, which is located at 0.68m
above the design waterline. The main dimensions of the ship and
model are given in Table 2 and Figure 1.
Experimental Setup The model is suspended at 30 degree drift angle inside the test
section by 8 wires, each 1.0mm in diameter. The forward and the
aft 4 wires are fixed at x/Lpp = 0.085 (frame 18) and at x/Lpp =
0.908 (frame 2), respectively, see Figure 2. A wind tunnel-based
coordinate system is applied. The origin is located at the
intersection of the waterline and forward perpendicular. The x-
axis coincides with the main flow direction. The y-axis is directed
toward the top. The z-axis points toward the sidewall of the
tunnel, at the opposite side of the PIV system, as required by a
left-handed coordinate system (shown in Figure 2).
Figure 2: Model and coordinate system.
At the forward perpendicular the model is equipped with a strip
of sand similar material to ensure the boundary layer transition at
this location. The blockage factor (ratio between the projected
areas of the double model and the cross section of the measuring
section) is about 0.026. The effect of blockage is not
homogeneous along the model. The distance between the model
and the sidewalls of the test section changes due to the drift angle
along the model. In the forward region of the model, the leeward
side is close to the wind tunnel ceiling. In the aft region, the
windward side comes close to the wind tunnel bottom. The
sidewalls of the test section are open and the ceiling and the
bottom are closed during the tests. Due to these special blockage
conditions, the velocity deviations in the far field of the model are
about 1% of the adjusted inflow wind speed.
Figure 1: Main model dimensions and Body plan of KVLCC2.
Table 2: Main dimensions.
Ship Model
Length over all LOA [m] 333.6 1.600
Length between perpendiculars Lpp [m] 320 1.535
Breadth (waterline) B [m] 58 0.279
Draft (original) T [m] 20.8 0.099
Draft (modified) D [m] 21.4755 0.103
Block coefficient CB [-] 0.8098 0.8098
Scale ratio [-] 1 208.5
Measuring Planes for the Velocity Measurements
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 4
Figure 3: Vortex system of KVLCC2 (isosurface of Q=200
colored by helicity) bottom view at β=30° [45] (top).
Regions of the experimental investigations (bottom).
Important regions for the local flow measurement are defined
based on the results of the numerical simulations published by
Xing et al. [45], see Figure 3. The results show that the flow is
dominated by three vortices. These are the Fore-Body Side
Vortex (FSV), After-Body Side Vortex (ASV) and After-Body
Bilge Vortex (ABV).
In order to capture the vortical flow structure, three regions for
the velocity measurements are defined. The flow in each region
is measured in vertical planes (perpendicular to the inflow
velocity). The three regions include the FSV, ASV and ABV, see
Figure 3. The marked planes at Figure 3 indicate width and height
of the measured regions. Their extent from the water plane of the
model (z = 0) is 200mm outwards.
A comparison between the experimental data and simulation
results is given in Section Results Planar Plots exemplary for the
section ASV-11.
Measuring Techniques PIV System
The spatial distribution of the velocity components in different
planes is measured by a modular commercial 2D-3C-PIV system
from TSI Inc.. The stereo PIV system (S-PIV) consists of a pulsed
laser, a light sheet optic, two cameras and a computer with
software to control image generation and processing.
The light sheet is generated by a 200 mJ two-head Nd-YAG laser
(Quantel Big Sky). Scattered light is received by two PowerView
4M (2048x2048 pixel, 12bit, monochrome) cameras equipped
with 105mm/F2.8 lenses; their baseline is located approximately
1.7m from the middle of the test section. The optical axes of the
lenses are inclined against the light sheet at angles of 62.5° and
41°.
For the PIV measurements, particles of an average diameter of
about 1 μm are generated as the seeding. The Laskin type droplet
generator uses dioctyl sehacate (DOS). The generator is placed
downstream of the test section. The fog generated spreads
through the wind tunnel at the closed loop operational mode and
leads to a global seeding. Therefore, any influence due to
turbulence of the generated fog is negligible.
LDA System
Additional velocity measurements are carried out using a one-
component LDA-system. The power of the Nd-Yag laser is 200
mW and the wavelength equals 532 nm. The tangential velocity
component to the hull sidewall Ut is measured at the planes in the
FSV and ASV regions. The velocity component is parallel to the
centerline of the model; this means the angle between the
measured velocity component and the free stream velocity is
equal to the drift angle (30 deg). The estimated uncertainty of the
measured velocity component is ± 0.20 m/s. The turbulence
degree is evaluated for this velocity component
Measuring Uncertainties
The PIV system is mounted on a crossbar, 2D automated traverse
system. The uncertainty of the positioning is ±0.1mm. The
estimated uncertainties of the three velocity components are Uw
= ± 0.08m/s, Uv = ± 0.06m/s and Uu = ± 0.33m/s. The relative
uncertainties of the velocity components to the free stream
velocity are Uw = ± 0.30%, Uv = ±0.22% and Uu = ± 1.22%. The
uncertainty of the 2D automated traverser system is estimated
based on a high number of repetition tests. The uncertainties of
the measured data by the PIV system are determined by the
dimensions of the measuring planes and the resolution of the
cameras as well as the selected time shift between two images.
Each measuring plane has about 50% overlap area with its
neighbors.
Flow Visualization
The smoke (vaporized oil) is injected to the wind flow near the
bow of the double model at different vertical and lateral positions.
The smoke distribution is recorded using a moving laser light
sheet for a sectional illumination. Stills (at the positions of the
PIV measuring planes) and movies are taken.
For visualizing the wall streamlines at the hull surface, a classic
oil film method is employed. The hull is coated uniformly with
oil mixed with sooty particles. As the wind tunnel starts, the oil
film on the surface moves in the direction of local shear forces.
After an order of 10’s of seconds, a nearly stationary particle
distribution is reached which appears as a sketch of the wall
streamlines. The evolving streamline pattern is recorded with a
Canon EOS 70D camera. The same camera is used to record the
smoke distribution. Stills are taken after shutting down the wind
tunnel to capture the final oil patterns reflecting the spatial
distribution of wall shear stress.
Experimental Results at Measuring Sections The experimental results include the flow visualization pictures
obtained by the smoke and classic oil film tests as well as the
velocity components in the measuring planes Ux, Uy, Uz in the
wind tunnel coordinate system and tangential velocity component
parallel to the hull surface Ut. The velocity components Uy, Uz
are used to calculate the longitudinal vorticity ωx. The fluctuation
of the velocity component (turbulence degree in [%]) is evaluated
as follows:
FSV
ASV
ABV
1 32 4
1 32 4 5 6 7
1 3 5 7 9
11 14
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 5
TUt= 100 × √(Ut
− Ut)2
/Ut,
where Ut is the instantaneous Ut.value and Ut its mean value.
The measured velocity components are normalized by the inflow
velocity. The analyses of the velocity vectors in the measuring
planes allow for identifying the particular vortex. The velocity
vectors can be used to identify the location and the strength of the
different vortices in the flow field. The results of the experimental
study will be discussed in detail in the results section.
CFD COMPUTATIONS
CFDShip-Iowa Setup The general-purpose CFDShip-Iowa-V.4 [3] solves the unsteady
RANS or DES equations in the liquid phase of a free surface flow.
The free surface can be captured using a single-phase level set
method, and the turbulence is modeled by isotropic or anisotropic
turbulence models. Numerical methods include advanced
iterative solvers, second and higher order finite difference
schemes with conservative formulations, parallelization based on
a domain decomposition approach using the message-passing
interface (MPI), and dynamic overset grids for local grid
refinement and large-amplitude motions.
Turbulence Models
The Algebraic Reynolds Stress (ARS) model [41] is based on a
modified version of Menter’s k- / k- turbulence model as the
scale determining model, and an explicit ARS model as the
constitutive relation in place of the Boussinesq hypothesis. The
ARS model is extended to ARS-DES models in CFDShip-Iowa-
V.4. The readers can refer to Xing et al. [45] for details of this
model.
Geometry, Boundary Conditions, and Simulation Domain
The domain extends (-2Lpp, 2Lpp) in the streamwise direction
(𝑥), (-1.5Lpp, 1.5Lpp) in the transverse direction (𝑦), and (-
1.2Lpp, -0.1Lpp) in the vertical direction (𝑧). The negative 𝑧
ensures that the entire ship hull is submerged in the water without
solving the level set transport equation. The top boundary is
specified as a “symmetry” boundary to mimic the double-body
model in the experiment. Body-fitted “O” type grids are
generated for ship hull and rectangular background grids are used
for specifying boundary conditions away from the ship hull, with
clustered grid near the symmetry boundary to resolve the flow
near the ship hull. As required by the turbulence models, 𝑦1+ <
1.2 is enforced for the first grid point away from the ship hull for
all the grids. The total number of grid points is 13 million, which
is much finer than Grid 3 used in [46]. The use of a 13-million
grid and DES model resolves 87% of the total TKE in the LES
region. An overview of the generated grid for the applied CFD
solvers is given in Table 4.
FreSCo+ and ReFRESCO FreSCo+ and ReFRESCO both originate from the FreSCo code
[40] that was developed within the VIRTUE EU Project together
with TUHH, Hamburg Ship Model Basin (HSVA) and MARIN.
After VIRTUE, two separate developments were continued:
FreSCo+ [30] by HSVA and the Institute for Fluid Dynamics and
Ship Theory (FDS) at TUHH; and ReFRESCO by MARIN.
These codes are generally similar and are described below.
The codes solve the multi-phase unsteady incompressible RANS
equations, complemented with turbulence models [44] and
volume-fraction transport equations for each phase.
The equations are discretized using a finite volume approach. The
procedure uses a segregated algorithm based on the strong
conservation form of the momentum equations. In ReFRESCO,
the mass and momentum equations can be solved in a coupled
manner as well.
A cell-centered, collocated storage arrangement for all transport
properties is employed. Structured and unstructured grids, based
on arbitrary polyhedral cells or local grid refinement with
hanging nodes, can be used. The implicit numerical
approximation is second-order accurate in space and time.
Integrals are approximated using the conventional mid-point rule.
The solution is iterated to convergence using a pressure-
correction scheme. Various turbulence-closure models are
available with respect to statistical (RANS) approaches. In both
codes scale-resolving (LES, DES) approaches are available as
well [28].
For ReFRESCO, several code verification studies have been
performed [6][7]. For maneuvering applications, several solution
verification and validation studies [35][36][37][38] have been
completed.
FreSCo+ Computational Setup
For the numerical calculation only one half of the double body
model is used in order to reduce the computational effort.
Therefore, the cutting plane is considered as a symmetry plane.
The size of the computational domain is 6L×6L×1.5L (L x B x
H). The hull has the same dimensions as in the experiment. The
walls of measuring section of the wind tunnel are not included in
the calculation.
Three unstructured grids are generated with the software
HEXPRESS. The grids have a refinement around the hull and in
the wake area, where the vortex structure will be formed. The drift
angle of β = 30° is taken into account. The typical cell size in
this region is reduced in two steps by a factor of √2. The detailed
values for the cell size and the number of cells of the grids can be
seen in Table 4. The y+value is kept constant for all grids and its
maximum value is y+= 1.2. In fact, the converged solution using
the same y+ for all grids may be different from the solution when
also refining the y+ upon grid refinement. Furthermore, y+=1.2
may be too large for SST, due to the very large gradients of ω
close to the wall, see [15].
In contrast to the wind tunnel experiment, in the numerical
calculation the fluid properties (density and viscosity) of water
are used. To achieve the same Reynolds number as in the
experiment the free stream velocity in the computation is set to
u = 1.785m/s. The calculations are performed with standard
k − ω and with the SST k − ω turbulence model of Menter 2003.
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 6
Unless otherwise noted, the results are presented for the finest
grid and Menter’s SST k − ω turbulence model.
An unsteady computation is also performed on the finest grid with
Menter’s SST k − ω turbulence model. The applied time step in
this calculation is dt=0.002s and the total simulation time is 12s.
The residuals (L1 norm) of unsteady calculation are three orders
of magnitude smaller than those of the steady calculation.
ReFRESCO Computational Setup
Multiblock structured O–O grids are used for this study for the
best performance of ReFRESCO. Grid points have been clustered
toward the hull surface and bottom to ensure proper capturing of
the boundary layers. The far field boundary is generated as a
cylindrical surface, to facilitate the use of a single grid for all
computations. The grids have been used previously for other
studies in which various water depths were studied [36][38]. The
diameter of the domain is 4Lpp and the bottom is located at about
2Lpp below the top surface. For all cases the y+ values in the first
cell from the wall are smaller than 1 for the finest grid, such that
the equations are integrated down to the wall. Grids have been
generated with GridPro. Based on these grids, geometrically
similar grids are generated by coarsening the finest grid in all
directions in order to assess the discretization errors and to
accelerate the iterative procedures by using coarse grid solutions
as initial flow fields for fine grid computations. Seven grids are
obtained, ranging from 121×103 to 12721×103 cells. Unless
otherwise noted, the results are plotted for the finest grid.
To simplify the calculations, symmetry boundary conditions are
applied on the undisturbed water surface. On the hull surface, no-
slip and impermeability boundary conditions are used. For all
calculations, the boundary condition on the bottom surface is set
to moving-wall/fixed slip (V=V∞, with V∞ the inflow velocity).
Since the computations were carried out prior to the wind tunnel
tests, some differences between the computational settings and
the wind tunnel setup are present. First, the loading condition of
the KVLCC2 corresponds to the normal loading condition (i.e.
T=20.8m). This means that the submergence of the hull is slightly
less than half the height of the wind tunnel model. Second, the
Reynolds number is slightly higher than that reached in the wind
tunnel: in the computations, the Reynolds number corresponds to
3.7 million. Third, the walls of the wind tunnel have not been
modeled in the grid and therefore blockage effects of the wind
tunnel are neglected. Computations have been conducted using
the 1994 [23] and 2003 [24] versions of Menter’s k-ω SST model.
The Spalart correction (proposed by Dacles-Mariani et al. [5]) of
the streamwise vorticity has been applied.
Edge FOI Edge Solver and Setup
Edge [8] is a three-dimensional Reynolds-averaged Navier-
Stokes (RANS) solver for compressible flows on unstructured
grids. The solver has an edge-based formulation and uses node-
centered finite volume techniques. The edge-based formulation
makes it possible to compute any arbitrary n-faced polyhedral
elements. The current version handles two types of surface
elements and four types of volume elements. The control volumes
are non-overlapping and are formed by a dual grid that is
computed by the pre-processor from the control surfaces for each
edge of the primary input mesh. Edge can be used for both steady
state and time accurate calculations. Time accurate computations
can be performed using a semi implicit, dual time stepping
scheme which exploits convergence acceleration technique via a
steady state from inner iteration procedure. A large number of
turbulence models are available that are categorized into three
different groups: RANS, Detached Eddy Simulation (DES) or
hybrid RANS-LES, as well as Large Eddy Simulation (LES).
Edge is the only compressible solver in this investigation and is
primarily developed by FOI with contributions from universities,
research institute and industry including Saab Aerospace and the
Royal Institute of Technology (KTH). More information is
available from the Edge homepage www.foi.se/edge.
For the KVLCC2 case, both time-accurate RANS (URANS) as
well as hybrid RANS-LES computations are run with Edge
version 5.2. The turbulence model selected for the URANS case
is the Wallin and Johansson [41] Explicit Algebraic Reynolds
Stress Model (EARSM) with the Hellsten k-ω model [11]. The
ship hull surface is modeled as an adiabatic weak wall boundary
condition with fully turbulent flow. A symmetry condition is
applied on the water surface to mimic the wind tunnel setup with
the double hull. All other surfaces are modeled as a far-field
boundary with a weak characteristic formulation. Standard day
conditions (NASA definition) are prescribed with a static
pressure of 101325 Pa, static temperature of 288 K and a free-
stream flow velocities of 27m/s with a drift angle of 30°. Thus,
no effect of wind tunnel walls is accounted for in the FOI Edge
computations. The low Mach number of 0.08 is a challenge for
any compressible solver and Edge has a pre-conditioning option
to overcome this. It is used to reduce the effect of too high
numerical dissipation. However, this was not applied in the
current investigation, which may have a negative effect of the
intensity and extend of the vortical flow. Otherwise, Edge default
input values are used.
The RANS case is initially run using a steady state approach with
local time stepping. However, due to oscillations in the solution,
a switch is made to a time-accurate RANS approach. The dual-
time scheme is set up using an implicit time step of 50 μs and 40
inner iterations. Initialization is done from the steady state RANS
and the solution is stabilized after 100 time steps but is continued
up to 1000 steps to fully develop force and moments. Mean-value
sampling starts after 300 time steps. For the hybrid RANS-LES
approach, the HYB0 method developed by Shia-Hui Peng
[26][27] at FOI is selected. The same dual-time scheme used in
the URANS case is used for the HYB0 case.
The computation is run with a three level multigrid cycle which
took approximately 3.5s/it on 128 cores on FOI’s J29 Linux
cluster. Also the HYB0 case is initialized from the RANS
solution and run for 1000 time steps before the mean-value
sampling starts for another 1000 time steps. The total
accumulated time for the HYB0 case is 0.1 s corresponding to
1.75 flow passes of the hull.
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 7
FOI Edge Mesh
The KVLCC2 mesh used for the Edge computations is a ship-
oriented, fully symmetric mesh. The unstructured mesh is
generated on the half-breath geometry and mirrored in the ship’s
symmetry plane to get a symmetric node distribution and scaled
to the wind tunnel model dimensions. FOI followed a two-step
approach to create the grid. In the first step, the ANSYS® ICEM
CFD™ was used to generate a patch dependent surface mesh and
from that make an initial unstructured volume mesh with the
Delaunay advancing front method. The far field was modeled as
a box, 3.75Lpp ahead, to the side and down of the model. The box
behind the ship is extended to 12.5Lpp. In the second step, FOI’s
in-house mesh generator TRITET [39] is used to build prismatic
boundary layers normal to the ship wall. A maximum of 34 layers
are added, layer by layer, with a first cell spacing of 5μm and a
prism expansion ratio of 1.22-1.25. The initial ICEM volume
mesh is used by TRITET to estimate cell sizes in the inner
domain. Any large volumetric steps are smoothed out in an
iterative process. The final tetrahedral volume mesh is built by
TRITET, starting from the outer boundary layer, with an
advancing front technique. The size and data on the FOI Edge
mesh is provided in Table 4.
FOI OpenFOAM OpenFOAM (Open Field Operation and Manipulation) is an
open-source CFD framework, licensed under the GNU General
Public License (GPL). OpenFOAM comes with basic meshing
tools, various solvers and utilities to import meshes and export
data for post processing. One of the strengths of OpenFOAM is
that customized solvers can be written or modified quickly
because of its modular design and the usage of advanced C++
features. The concept of object-oriented programming allows
OpenFOAM solvers to be written as a hierarchy of classes and
functions that are related to datasets and operations. These classes
and functions can be deemed as e.g. variable fields, mesh,
boundary conditions, numerical operators, etc.
In this study, the incompressible LES solver developed by FOI is
used [42]. LES is based on the idea of separating scales and
dividing the flow into two regimes by means of a low-pass filter
applied to the Navier-Stokes Equations (NSE) with a cut-off
length based on the grid size ∆. The first regime, composed of the
large-scale eddies and properly resolved on the grid, is computed
using a space-time accurate algorithm. The other regime,
containing the small unresolved eddies and ranges from the filter
cut-off down to the Kolmogorov scales, results in an additional
subgrid term, ∇ ∙ B, in the LES momentum equation that must be
modeled, [31], where B = (v ⊗ v − v ⊗ v) is the sub-grid stress
tensor, with v being the velocity and the overbars denoting the
low-pass filtering.
The direct simulation of the large, energy-containing eddies
(being geometry and flow dependent) gives LES much more
generality than RANS, in which the full spectrum of the
turbulence is modeled. The physics of the small-scale, unresolved
flow, or rather the effects of this on the resolved flow, have to be
represented by sub-grid models. However, since only the small-
scale flow is subject to modeling, the assumption is that more
universal models can be adopted. A common criterion for LES is
that at least the energy of the flow is resolved, see [29]. For the
LES computations reported herein, approximately 95% of the
turbulent kinetic energy of the flow is resolved, and accordingly
these simulations can be considered trustworthy.
OpenFOAM Computational Setup
Regarding the sub-grid modeling in LES, it is common to
differentiate between functional and structural models [31].
Functional models aim at reproducing the effects of the small,
unresolved flow on the resolved flow [21][34]; whereas structural
models aim at estimating the sub-grid flow physics based on the
nature of the resolved flow physics and appropriate scaling laws
[1][19][22]. In this study the Mixed Model (MM) is used, which
is composed of one scale similarity term and one eddy viscosity
term [1]. The model coefficients are obtained by integrating the
energy spectra [31], or through a dynamic procedure [10][16].
The longitudinal vortices with a characteristic length and spacing
dominate dynamically the eddy scales and the flow close to solid
wall. The longitudinal vortices have W-shaped vortex structures
that interact with the bulk flow. The scales dominating the near-
wall flow scale with the Re number are typically much smaller
than those of the free flow. Simulating wall-bounded flows with
LES is thus a challenge, since either the near-wall flow structures
need to be resolved, i.e. wall-resolved LES, or the influence of
the near-wall flow needs to be modeled, i.e. wall-modeled LES
[14].
The preferred model for complex geometries is based on the LES
boundary-layer equations, the solution of which, μt and νy+ is
employed to modify the viscosity. The superscript + denotes
viscous scaling, and ν is close to the wall so that νeff = ν + νk = ρτω/du/dy = ρμτ y+/ν+ [9]. This model can be combined
with any other sub-grid model such as the MM used here.
OpenFOAM is based on an unstructured collocated finite volume
method based on Gauss’s theorem together with a multi-step
time-integration method [17]. For LES, the time-integration is
performed using a semi-implicit second-order two-point
backward-differencing scheme. Convective fluxes are
reconstructed using multidimensional cell-limited linear
interpolation, whereas diffusive fluxes are reconstructed using a
combination of central difference approximations and gradient-
face interpolation to minimize the non-orthogonality error. The
Pressure Implicit with Splitting of Operators (PISO) method is
used to discretize the pressure-velocity coupling [13]. The
scheme is second-order accurate in space and time, and the
equations are solved sequentially, with iteration over the explicit
source terms, with a Courant number of approximately 0.4.
FOI OpenFOAM Mesh
The OpenFOAM mesh is generated using ANSYS®ICEM
CFD™. To account for the drift angle, the ship hull is rotated
around the forward perpendicular (FPP), keeping the outer free
stream box fixed. The boundaries of the free stream are located
three hull lengths upstream, below and to the sides. The out-flow
boundary is located ten hull lengths downstream. The wake in the
mesh is adapted to the drift angle using density boxes in the
expected wake region. The original full-scale KVLCC2 hull
geometry, with an Lpp of 320m, is obtained from the SIMMAN
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 8
2014 web site [33]. The final mesh is scaled to the TUHH wind
tunnel model dimension with an Lpp of 1.535m.
The mesh generation process starts with the creation of a patch-
dependent triangular surface mesh on the hull. Careful attention
is taken to ensure a smooth transition of cell sizes between and
inside each patch. A global cell size of 1 is specified. The bow
cell size of 0.2 is blended with an exponential expansion ratio of
1.07 into a mid-ship size of 0.5 down to the smallest size of 0.05
at the stern. The waterline boundary is split into patches to match
the density box in the wake region. The dimensions of the wake
density box are set individually for each drift angle and locally
aligned with the expected flow one hull-length downstream of the
stern with a similar draught and breadth as the hull. The
expansion ratio is set at 1.07 away from the hull towards the far
field with a maximum size of 20. An intermediate tetrahedral
volume mesh is generated using the Delaunay advancing-front
method with a spacing-scaling factor of 1.15. From this mesh, 10
prismatic layers are added to the hull surface mesh with an
expansion ratio set at 1.15 without specifying initial or total
height. ICEM CFD thereby adapts each layer to the local cell size
with thinner layers where cell sizes are small. The final
tetrahedral volume is again generated using the Delaunay
advancing-front method but this time with the expansion ratio
lowered to 1.07.
At the inflow boundary, Dirichlet conditions are used for the
velocity and sub-grid kinetic energy, whereas a zero Neumann
condition is used for the pressure. At the outlet, zero Neumann
conditions are used for the velocity and sub-grid kinetic energy,
whereas a Dirichlet condition is used for pressure. No-slip
conditions are used at the hull surface and free stream conditions
are used at the remaining boundaries.
NavyFOAM NavyFOAM employs a cell-centered finite-volume spatial
discretization which permits use of arbitrarily unstructured
polyhedral meshes including hexahedron, tetrahedron, prism and
wedge to name just a few. The linear gradients of the flow fields
can be computed using either the Green-Gauss theorem or least-
square fitting of the neighboring cell data. A large number of
convection discretization schemes are available, including high-
order upwind-biased schemes. Among them, the second-order
upwind scheme is both sufficiently accurate and robust, being
adequate for Reynolds-averaged Navier-Stokes (RANS)
computations of industrial flows. The diffusion terms are
discretized using a second-order central-difference scheme. All
the spatial discretization schemes, including the flux interpolation
schemes, are formally second-order accurate for arbitrary
polyhedral grids. An implicit, segregated, iterative projection
algorithm is employed for time-advancement of solutions. The
system of linear equations resulting from the discretized
governing equations are solved using a choice from the iterative
solvers such as Gauss-Seidel, diagonal incomplete Cholesky
(DIC), preconditioned conjugate gradient (PCG) or generalized
geometric multigrid (GAMG) methods.
NavyFOAM offers a suite of RANS turbulence models including
the k-ε and k-ω families of linear and non-linear eddy-viscosity
models and Reynolds-Stress Transport Model (RSTM).
NavyFOAM also has several subgrid-scale (SGS) turbulence
models for large eddy simulation (LES) and hybrid RANS-LES
models. NavyFOAM offers an adaptive, two-layer wall function
that can handle both near-wall-resolving (y+ = 1) and near-wall-
modeling grids.
NavyFOAM Computational Setup The computational domain with the size of
[5.69Lpp×0.98Lpp×1.3Lpp] is bounded by an upstream inlet, the
tunnel wall, a downstream exit and symmetry boundary
conditions at the symmetry plane of the double hull model. Note
that we have decided to include the tunnel wall in light of
potential blockage effects. Only a half of the full domain is
modeled, assuming that the flow remains symmetrical with
respect to the symmetry plane of the double-body. A hex-
dominant unstructured grid with 77 million volume elements is
used for the computation. We deliberately choose to employ the
wall function approach to evaluate its efficacy in resolving the
turbulent boundary layer and three-dimensional flow separation.
The y+ at the centers of the wall-adjacent elements of the grid
ranges between 40 and 100. The effects of the tunnel wall-shear
are included using a fairly coarse near-wall resolution. A block of
grid with 6 levels of refinement is embedded around the hull to
resolve the hull boundary layer, cross-flow separation, free vortex
layer, and multiple vortices in the near-body region. A steady
RANS solver in NavyFOAM is used for the computation using
the high Reynolds number version of Wilcox’s k-ω model [43].
ANALYZING METHODS
Forces In order to analyze the hydrodynamic forces acting on the ship
body, the following normalizations are used for the forces in x-
and y-direction and the yaw moment around the midship:
𝑋′ =𝐹𝑥
12𝜌∙𝑈2∙𝐿∙𝑇
, 𝑌′ =𝐹𝑦
12𝜌∙𝑈2∙𝐿∙𝑇
, 𝑁′ =𝑁𝑧
12𝜌∙𝑈2∙𝐿2∙𝑇
U is the inflow velocity. The forces (𝑋′ and 𝑌′) and the yaw
moment (𝑁′) are given in ship coordinate system.
Procedure of Vortex Core Analysis For the three main vortices FSV, ASV and ABV, a detailed vortex
core analysis is carried out. The aim of the analysis is to calculate
some reference parameters in order to carry out an accurate
comparison between the measured and calculated results as well
as between the different numerical methods. The reference
parameters for the comparison with measured values are the
location of the vortex core, the axial vorticity component and the
axial velocity component. These values can be obtained from the
wind tunnel measurement data as well as the CFD results. The
comparison of the vortex parameters includes some parameters
that are determined by analysis of the CFD results such as: Q-
value, the pressure and the TKE at the core of each vortex. The
results of CFDShip-Iowa, FreSCo+, ReFRESCO, Edge-EARSM
and Edge-HYB0 are considered in the analysis. Identifying the
position of the vortex core can be accomplished by analyzing the
location of the maximum axial vorticity component or the
maximum of Q-value. The location of the axial vorticity
component and the maximum of Q-value are evaluated in
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 9
different sections perpendicular to the inflow direction for the
different vortices. In most cases, the determined core positions
based on maximum ωx or Q are identical or the differences are
negligible. To verify this fact the coordinates of the core position
of the vortices FSV, ASV and ABV are identified in the results
of FreSCo+ according to the two different criteria. In the
presented analysis results the location of the vortex core in the
EFD results and in the CFDShip-Iowa are determined based on
the axial vorticity component, while the maximum of Q-value
criterion is considered by the evaluation of the results of FreSCo+,
ReFRESCO, Edge-EARSM and Edge-HYB0.
The above-mentioned parameters of the core vortex analysis are
made dimensionless by using the inflow velocity and model
length as follows:
𝑦𝑐𝑜𝑟𝑒: core y-location, normalized by 1/𝐿𝑝𝑝, measured from the center line
of the double body,
𝑧𝑐𝑜𝑟𝑒: core z-location, normalized by 1/𝐿𝑝𝑝, measured from the symmetry
plane of the double body,
𝑄𝑝𝑒𝑎𝑘: maximum Q-value, normalized by 𝐿𝑝𝑝2/𝑈∞2 ,
𝜔𝑥,𝑐𝑜𝑟𝑒: core axial vorticity, normalized by 𝐿𝑝𝑝/𝑈∞ ,
𝑈𝑥,𝑐𝑜𝑟𝑒: core axial velocity, normalized by 1/𝑈∞ ,
𝑐𝑝𝑐𝑜𝑟𝑒: core pressure, corrected for free stream pressure and normalized by
1/(0.5 ∙ 𝜌 ∙ 𝑈∞2 ),
𝑇𝐾𝐸: turbulent kinetic energy, normalized by 1/𝑈∞2 .
The core vortex parameters are plotted over x/Lpp in all
corresponding diagrams, where x points in the wind tunnel main
flow direction and the origin is located at the forward
perpendicular. Figure 11 show the results of the FSV, the ASV
and the ABV. The location of the measuring sections FSV-1,
FSV-2, ASV-1, ASV-6, ASV11, ABV-1 and ABV-2 are marked
in Figure 11. The distribution of axial vorticity and distribution
of axial velocity in the selected measuring sections are presented
in Section: Results.
Additionally, a verification and validation (V&V) analysis [4] for
the three main vortices (FSV, ASV, ABV) is carried out. The
errors are only calculated for the measuring sections were both
CFD and EFD data are available. The error (E) between CFD (S)
and EFD (D) is expressed by following formula:
|E(%D)| = |S−D
D× 100|.
Here, the absolute formulation of the error is used because an
averaged value is considered for the V&V analysis. Signed values
might lead to a too small error. The values can be found in Table
6, Table 7 and Table 8.
Planar Plots Further comparison of the measured and calculated results is
given in Figure 12. The figure includes the following values: 𝑈𝑥,
𝑈𝑦 , 𝑈𝑧, 𝑈𝑡, 𝜔𝑥, 𝑇𝑈𝑡 and TKE.
The values are normalized as mentioned before. It should be
noted that figures with TUt exist only for the wind tunnel
measurements. The TKE data is only available for the simulations
of FOI-Edge, TUHH and MARIN.
RESULTS
Forces and Yaw Moment An overview of normalized force and yaw moment coefficients
obtained by the numerical methods is given in Table 5. Due to a
lack of data for the force measurements in the wind tunnel, the
RMS-values of all CFD simulations are used for further
comparison. Only the computations with the finest grid and
different turbulence models of each code are considered. The
corresponding simulations are marked in Table 5. For the global
forces and moments comparison, the deviations of CFD results
from the RMS value are calculated as follows:
𝐷(%𝑅𝑀𝑆) =𝑆−𝑅𝑀𝑆
𝑅𝑀𝑆× 100.
The calculated X-force by CFDShip-Iowa using ARS-DES is
higher than other applied turbulence modeling techniques. The
simulation results of Edge-EARSM also deliver high X-force.
The lowest value is obtained by OpenFOAM-LES. The
calculated values of X-force using two-equation-based turbulence
modeling are close to each other.
The calculated Y-force by CFDShip-Iowa using ARS-DES is
higher than other applied turbulence modeling techniques. The
lowest value is obtained by Edge-HYB0. The calculated values
of Y-force using two-equation-based turbulence modeling are
also close to each other.
The calculated N-moment by CFDShip-Iowa using ARS-DES is
also higher than other applied turbulence modeling techniques.
The lowest value is obtained by OpenFOAM-LES.
Although extensive V&V studies are not carried out, some
comments are given on the presented results. The ARS-DES (13
M nodes) model delivers the highest and the LES-MM (36.5 M
nodes) the lowest value. The results of the two-equation
turbulence models such as standard k-ω or SST k-ω show a
decrease in magnitude of the calculated X-force coefficient when
increasing the grid resolution, see Table 5. The percental standard
deviation with respect to the RMS value (SD%RMS) is 72% for
the X-force, 8.3% for the Y-force and 11.6% the N-moment.
Vortical Structures and Vortex Core Analysis Figure 4 shows the visualized flow on the model at different
stations. The three main vortices, Fore-Body Bilge Vortex (FBV),
Fore-Body Side Vortex (FSV) and After-Body Side Vortex
(ASV), can be clearly identified. Where the Fore- and the After-
Body Side Vortices are elongated (the axis parallel to the ship
bottom is longer than the axis perpendicular to it), the cross
section of the Fore-Body Bilge Vortex has nearly a circular shape.
As mentioned before, the investigation is carried out for a double
model. Therefore, the FSV exists in Figure 4 twice: one
developed due to the interaction of the flow with the front half of
the double model and other FSV by the interaction with the
second half of the model. Both FSVs induce a transverse velocity
component in symmetry plane, which is directed to the model
sidewall, as can be clearly seen in the plane shown in Figure 4. It
is difficult to achieve an exact symmetry condition between the
ship and inflow in the experimental setup in the wind tunnel,
therefore it can be seen that the induced flow by the FSVs is not
fully symmetric.
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 10
Figure 4: Visualization of the Fore-Body Side Vortex (FSV) in
the wind tunnel, blue arrows indicate the flow /
rotation directions.
The results of visualization of the flow in the wind tunnel are
documented in black white photos. The grey color in the photos
can be analyzed and assigned to a grey scalar. This scalar can be
translated to colored scalar that shows the vortical structure, see
Figure 4. Unfortunately, it is not possible to define the
corresponding Q-value for each color. Therefore, only the main
shape of the vortex structure can be compared irrespective of the
absolute Q-value.
An overview of the vortical structure is given in Figure 5. The Q-
criterion is applied to identify the vortical structures [12]. The
criterion is based on the second invariant of velocity gradient
tensor ∇u. Q is made non-dimensional using Q´=Q*L2/V2. For
simplicity the dash over the non-dimensional quantity Q´ will be
omitted. However, the Q-criterion cannot be used to visualize the
orientation of the detected vortex. To overcome this weakness,
the normalized helicity density [20] is proposed as follows:
𝐻𝑛 =𝑈∙𝜔
|𝑈|∙|𝜔|
where U and ω are the velocity and vorticity vector at the same
point. The normalized helicity density Hn will be applied to color
code the Q-isosurface in the current study. It represents the
directional cosine between the vorticity vector and the velocity
vector, −1 ≤ Hn ≤ 1. The sign of Hn indicates the direction of
swirl of the vortex relative to the streamwise velocity component.
The flow structure around the model can be characterized in
Figure 5 (Q=200) by the following vortices:
1. Fore-Body Bilge Vortex (FBV), Leeward
2. Fore-Body Side Vortex (FSV), Leeward
3. After-Body Side Vortex (ASV), Windward
4. After-Body Bilge Vortex (ABV), Leeward
5. Stern Vortex (SV), Leeward
6. Aft-Body Hairpin Vortex (ABHPV), Leeward
7. Kelvin-Helmholtz Vortices (KH), Leeward
8. Karman-like Vortices (KL), Leeward
The nomenclature of the above vortices follows the suggestion
given by Xing et al. [45].
Figure 5: Predicted vortical flow structure for Q=200,
analyzed based on the FreSCo+ results:
In general, the flow field is dominated by the strong interaction
that takes place between the different vortices, see Figure 8 and
Figure 9. The comparison between the instantaneous and the
mean simulation results facilitates a deep insight into the detail of
this interaction, particularly in the stern region. Figure 8 shows
the structure of Q=100 based on the mean values of the final 1000
iterations of the Hybrid RANS-LES (HYB0) and the LES-MM
simulations. The instantaneous structure of Q=100 is shown in
Figure 9. In the present study, the structure of different vortices
will be discussed focusing on the FSV, ASV and ABV vortices.
FSV, ASV and ABV show open-type cross-flow separation from
the hull. The vortices separate as a circular type, undergo helical
mode instability, and transform into spiral vortices, as shown in
Fig. 3(top). As the vortices progress, the vortex core axial velocity
and vorticity decreases, and pressure and TKE increases. The
swirl ratio S =𝑈𝜃/𝑈𝑥, where 𝑈𝜃is the tangential velocity and 𝑈𝑥
is axial velocity, is S~0.5 (CFDShip-Iowa) and S~0.6 (FreSCo+)
at the inception of the spiral streamline. The dominant frequency
f along the vortex core, evaluated using pressure fluctuation in the
vortex core, show that the St =fL/U0 decreases with the
progression, where U0 is free-stream velocity and L is ship length.
The scaling of the dominant frequency using the distance from
the origin of spiral streamline location X shows for instability
analysis of the CFDShip-Iowa result that St decreases with the
progression of the vortices, and is StX = 1.2 ~ 1.3 for FSV, StX =
1.35 ~ 1.45 for ASV and StX = 1.8 ~ 2.25 for ABV. Xing et al.
[45] referred to the transformation of circular to spiral vortices as
vortex breakdown.
Figure 6 shows streamlines in the vortex core and the location of
helical instability inception (black points) for the FreSCo+ results.
ASV
FBV FSVFSV induced
flow
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 11
Figure 6: Predicted vortical flow structure for Q=200 with
vortex core streamlines and location of helical
instability inception (black points), based on the
FreSCo+ results.
Spiral vortices have been reported for swirling jets [47], wing tip
vortices [25] and delta wing leading edge vortices [50]. In these
cases, circular vortices exhibit vortex breakdown followed by
helical mode instability and transformation into spiral vortices.
The breakdown is characterized by a sudden expansion of the
vortex core and sharp gradients in vortex core variables, i.e., drop
in axial velocity and vorticity, and increase in pressure and TKE
[25]. The initiation of the vortex breakdown occurs if the swirl
ratio is higher than the critical value Sc. The critical value
depends on the flow type, Re, inflow condition, swirl angle with
respect to jet axis etc. [48]. Spall et al. [51] showed that Sc
decreases with Re, i.e., Sc = 2 to 3 for Re < 100, and 1.6 for large
Re > 104 for wing tip vortices. For delta wings, Sc ~ 1 for range
of Re, as shown by Greenwell [48] for a range of delta wing
vortex configurations. For delta wings, the helical mode
instability frequency is inversely proportional to the distance
from the breakdown location. Thus, StX is constant along the core.
Gursul [49] reported that StX ranges from 0.75 to 1.35 for large
sweepback delta wings at different flow conditions.
The vortices for KVLCC2 at β = 30 have similarities with the
swirling jet or delta wing vortices as they show helical mode
instability, spiral streamlines/vortices, high swirl at instability
inception, and Stx range is consistent with those of delta-wings.
However, the swirl ratio is lower and large differences in
transition process from circular to spiral vortices. For swirling jet
or delta wing vortices, the transition process is abrupt with large
change in vortex size and gradients of the vortex core variables,
i.e., vortex breakdown. For ship flows, the onset/transition
process is abrupt but without large change in vortex size and
differences in gradients and trends of the vortex core variables.
Nonetheless, we retain the terminology vortex breakdown for this
process. The differences between ship and aero flows likely due
to global geometry and pressure gradients and the interaction of
the ship vortices with the boundary layer and other vortices.
Fore-Body Side Vortex (FSV)
As can be seen in Figure 8 and Figure 9 the FSV is developed on
the leeward side of the forward part of the ship hull. The distance
from the vortex center to the sidewall as well as to the hull bottom
grows with increasing x/Lpp-value, see Figure 11. In the stern
region, the coordinates of the core center follow the contour of
ship sidewalls. The measured y- and z-coordinates of the vortex
center are included in Figure 11. It can be seen that the calculated
coordinates of the vortex center agree well with the measured data
in the range of x/Lpp 0.25 to 0.7. Unfortunately, no experimental
results are available after x/Lpp=0.7. The calculated y-
coordinates by the different codes in the x/Lpp range between 0.7
and 1.0 and show some differences, see Figure 11. The obtained
y-coordinates in this range by the Edge Hybrid RANS-LES
HYB0 simulation are smaller than the values calculated by RANS
simulations using two-equation models.
The instantaneous pattern of the FSV is shown in Figure 9: the
width of the vortex pattern obtained by FOI OpenFOAM
increases with the growing run length of the vortex. In all
numerical simulations the diameter of the vortex increases along
its run length. FreSCo+ results show a high increase of the vortex
diameter, see Figure 8. The limited grid resolution in this region
may be responsible for the increase of the vortex diameter.
In Figure 8 a vortex sheet that surrounds the FSV can be clearly
seen. Most of the CFD computations predict these secondary
vortices, but the shape of the vortical structure shows different
characteristics. NavyFOAM and the time-averaged FOI
OpenFOAM predict a vortex sheet that spirals around the FSV
vortex axis and the spiraling vortex lines are inclined to the FSV.
Nelson and Pelletier [25] have experimentally investigated the
behavior of similar vortex structure on the leading edge of delta
foil and have reported that vortex sheet induces an axial flow in
the downstream direction of the vortex. This observed flow
behavior is confirmed by the measured data for the longitudinal
velocity component in the vortex core, as can be seen in Figure
11. This tendency is captured well by the simulation results of
CFDShip-Iowa using ARS-DES for a certain range of x/Lpp. The
flow acceleration is not captured by the other codes.
The time-averaged results of FOI Edge-HYB0 and ARS-DES
CFDShip-Iowa also show the secondary vortices structure, but
the spiraling vortex lines around the FSV are less pronounced.
The vortex sheet can be also be seen in the results of FreSCo+ and
ReFRESCO. The structure obtained by FreSCo+ also shows
spiraling vortex lines that are inclined relative to the FSV, but the
inclination direction is not in accordance with the results obtained
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 12
by the other codes. Further computations are carried out to
analyze this problem. The shape of the vortex sheet calculated by
FreSCo+ using steady case has no physical meaning: as the
computation switched from steady to unsteady, the shape of the
vortex sheet was changed. The new results are similar to
ReFRESCO results. This means the vortex sheet around the FSV
exists and has a smooth surface, see Figure 8.
The secondary vortices structure and the spiraling vortex lines
around the FSV are also predicted by the NavyFOAM using the
k-ω model (Wilcox 2008 [43]) in combination with wall function
(y+ between 40 and 100). The NavyFOAM computation is
carried out on a quite fine grid using an isotropic turbulence
model. This secondary vortex structure is also visible in the
results using the anisotropic turbulence model such as Edge-
HYB0 or ARS-DES CFDShip-Iowa as well.
The Q-values show that two peaks exist, see Figure 11. The first
one takes place between x/Lpp 0.25 to 0.3 and the second one in
the x/Lpp region between 0.95 and 1. The first peak is much
larger than the second one. Between the two peaks there is a
continuous reduction of the Q-value. The second peak may be
induced by other vortices existent in the after-body region. The
results obtained by FreSCo+, ReFRESCO, Edge-EARSM and
Edge-HYB0 show the same tendency over a wide range. At x/Lpp
>0.9 the Q-values by FreSCo+ start to decrease faster than the
other method; the reason may be the limited resolution of the used
grid in this region. The calculated values by Edge-HYB0 are in
general lower than the result of the FreSCo+ and ReFRESCO but
they follow the same tendency. The Q-values along the model by
Edge-EARSM are much lower than the above-mentioned three
codes. Behind the ship model the Q-values by Edge-EARSM are
low but it is still in the range obtained by Edge-HYB0 and
FreSCo+.
The variation of the longitudinal vorticity (ωx) along the non-
dimensional x-axis is presented in Figure 11. While all numerical
simulation methods show a continuous reduction of ωx in the
x/Lpp range higher than 0.3, the measured ωx show an increase of
the in the range between x/Lpp=0.3 and 0.4 and after the position
of x/Lpp=0.45 the measured ωx value remains constant until
x/Lpp=0.7.
In order to understand the reason for the different behaviors of the
measured and calculated ωx, it is important to consider the
characteristics of the flow surrounding the FSV. This vortex
arises in the boundary layer of the model, leaves the boundary
layer very fast and progresses in the outer flow region. The
influence of shear flow and the associated diffusion play a minor
role in the outer flow region. Therefore, the main part of the FSV
can be considered as an isolated vortex with negligible interaction
with the surrounding outer flow and these circumferences allow
the vortex to keep its strength over quite a long distance. The
measured vorticity increases after passing the aft shoulder; this
may be due to the interaction with other vortices in this region.
The calculated axial vorticity in all simulations shows a contrary
tendency to the measured results. The calculated ωx decays along
the x/Lpp. This fact is valid for simulations based on the isotropic
as well as the anisotropic turbulence modeling. As mentioned
before, while the measured results show a concentrated vortex in
the outer flow, which keeps its strength for a long distance, the
simulations cannot reproduce this tendency.
The helical instability according to the prediction presented in
Xing et al. [45] takes place at a position x/Lpp=0.32 close to FSV-
1 section. It can be seen that there is a steep reduction of the ωx
calculated by CFDShip-Iowa at this location. A similar behavior
can be seen in the results of Edge-EARSM, but this reduction
exists much earlier at the position x/Lpp=0.22.
The comparisons between the calculated pressure coefficient and
TKE are presented in Figure 11. With exception of CFDShip-
Iowa code the other applied methods predict the minimum
pressure coefficient at nearly x/Lpp=0.32, which agrees with the
predicted position of the helical instability by in Xing et al. [45].
The absolute value of the minimum pressure varies over a wide
range; the lowest is about -1.65 predicted by FreSCo+ and the
highest is -1.0 by Edge-EARSM. The results of the other codes
lie within this range. The CFDShip-Iowa results follow the same
tendency, but they have two peaks located between 0.4 and 0.6
that cannot be seen in the results of the other codes. The
calculated pressure coefficients by ReFRESCO, Edge-EARSM
and Edge-HYB0 in the x/Lpp range higher than 0.8 show two
peaks. The location of the first peak calculated by ReFRESCO
agrees well with FreSCo+ results. The comparison of the TKE
values shows that they are nearly close to each other at the
beginning of the FSV. With increasing x/Lpp value, the
calculated TKEs by CFDShip-Iowa and ReFRESCO decrease
while the TKE values by FreSCo+ and Edge-HYB0 show a
continuous increase. FreSCo+, Edge-EARSM and Edge-HYB0
predict a continuous increase of TKE after x/Lpp=0.7. In this
location the vortex changes its y-coordinates and moves in the
direction of the sidewall of the hull. In the stern region, the
calculated TKE values show a maximum value followed by a
steep reduction. The predicted location of the maximum TKE
value by the different codes varies between x/Lpp=0.9 and 1.1.
The calculated maximum in the stern region shows a wide
variation. The lowest value is obtained by ReFRESCO and the
second highest value is calculated by FreSCo+, although both
codes use the same turbulence model. The highest TKE value is
obtained by Edge-HYB0 at x/Lpp=1.07.
After-Body Side Vortex (ASV)
The ASV dominates the flow on the model bottom beginning at
the windward forward shoulder along the chine. At circa
x/Lpp=0.55 the vortex changes its direction and follows more or
less the free stream direction. This effect can be clearly seen in
Figure 8 and Figure 11, which show the y-position of the ASV
core along the hull. Considering Figure 8, where the vortices have
been visualized by the Q-criterion (Q=100), the ASV seems to be
most clearly pronounced in the results of NavyFOAM and
FreSCo+ followed by CFDShip-Iowa, ReFRESCO and FOI Edge.
In the FOI OpenFOAM results the vortex is the least pronounced.
This applies to both the averaged and the instantaneous results. It
is important to notice that on the windward side of the ASV a
smaller contra-rotating vortex exists, which seems to turn around
the ASV. This vortex becomes visible in the region of
x/Lpp=0.55, where the ASV changes its direction. The
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 13
NavyFOAM results show that ASV, after a short distance, splits
into two parallel running vortices, see Figure 8. Similar flow
behavior can be seen in the FreSCo+ results. The split vortices are
also clearly visible in the planar data comparison. Due to the
complexity of the ASV system, it forms different separation and
reattachment lines on the hull bottom, as discussed in Section
Results: Limiting Streamlines.
Figure 11 shows the variation of ASV core position beside and
below the hull. All CFD simulations predict the y-position very
well over the whole x-range considered by the wind tunnel
measurement. After x/Lpp=0.95, the numerical results show two
different tendencies. While the results of ReFRESCO, Edge-
EARSM and Edge-HYB0 predict a direction change of the vortex
core, in the results of FreSCo+ and CFDShip-Iowa the ASV keeps
its direction. Unfortunately, no measurement data is available in
this region.
The predicted z-position by the different solvers for the ASV is
more or less the same until x/Lpp=0.7. After this position, it can
be seen that different trends are predicted. While the results of
ReFRESCO, Edge-EARSM and Edge-HYB0 predict a steep
moving of the vortex core upward, a moderate raise of the vortex
core can be seen in the results of FreSCo+ and CFDShip-Iowa.
At the beginning, the vortex stays very close to the bilge region
and starts to move away when it comes near the aft shoulder
(x/Lpp=0.55), where it changes its y-direction and crosses the
hull. The deepest point is then reached at about x/Lpp=0.65-0.7,
where ASV separates from the hull. The lowest position predicted
by FreSCo+ is in good agreement with the measurement. The
CFDShip-Iowa predicts the lowest position only after the vortex
has separated from the hull. Before the separation point, the
location of the vortex core stays closer to the hull than the
measured values.
The calculated Q-values in the vortex core along the hull are
presented in Figure 11. The results of ReFRESCO and FreSCo+
have a similar tendency regarding the rate of the reduction of Q-
values over x/Lpp. While the results of ReFRESCO show an
oscillating behavior, the FreSCo+ results are smooth. The
predicted Q-values by Edge-EARSM and Edge-HYB0 are
similar, and behind x/Lpp=0.7, the gradient of the reduction of Q-
values over x/Lpp is much steeper compared with results of
ReFRESCO and FreSCo+.
The vorticity (ωx) in the vortex core along the hull is depicted in
Figure 11. As the FSV is strongly influenced by the shear flow in
the boundary layer region on the ship bottom. The calculated
values show a continuous decrease of the vorticity over x/Lpp.
The measured results confirm the calculated tendency shown by
the applied numerical methods. The absolute values of
computation results are in good agreement with the measurement.
The CFDShip-Iowa and Edge-HYB0 predict a steep decrease of
ωx at x/Lpp=0.55. This local strong reduction cannot be seen in
the results of Edge-EARSM, ReFRESCO and FreSCo+, which
use the two-equation turbulence model.
The identified position of helical instability by Xing et al. [45] is
x/Lpp=0.72, which is close to the position where the vortex has a
strong change of its y-direction. The measured data also show a
local reduction of ωx in this region.
Figure 11 shows the comparison of the axial velocity component.
It can be noticed that the calculated values agree well and they
follow the measured values. However, the measured axial
velocity component is about 0.2 higher than the calculated values.
The reason for this difference is not clear; it may be due to the
fact that the accuracy of the PIV measurement of the axial
velocity component very close to the ship bottom suffers from the
surface reflection in this region.
Figure 11 includes the comparison for the pressure coefficient
and the TKE, respectively. While CFDShip-Iowa, Edge-HYB0
and Edge-EARSM show a strong variation of the pressure
gradient along the vortex core, the results of ReFRESCO and
FreSCo+ show more or less a continuous decrease of the pressure
coefficient. In the region of x/Lpp=0.4, the predicted pressure
coefficient varies a lot: FreSCo+ delivers the highest and Edge-
HYB0 the lowest one. The results of Edge-EARSM are located
in between, as expected.
The calculated level of the TKE by the applied methods at the
beginning of the ASV is different. The TKE obtained by FreSCo+
is much higher than the ReFRESCO values, although the same
turbulence model is applied in the both simulations. The
calculated maximum TKE values by Edge-EARSM are higher
than FreSCo+. The calculated results by ReFRESCO and Edge-
HYB0 are nearly in the same range and much lower than the
Edge-EARSM and FreSCo+ results. The calculated TKE by
CFDShip-Iowa at x/Lpp=0.6 are close to the results of Edge-
EARSM and FreSCo+, and after this position the TKE falls down
to the level obtained by ReFRESCO and Edge-HYB0. The results
of all methods show an increase of the TKE nearly at the same
position, around x/Lpp=0.88. Comparing Figure 11, it can be seen
that after the identified position of helical instability by Xing et
al. [45], a strong local increase of the pressure coefficient and the
TKE take place. Both are an indication for helical instability.
After-Body Bilge Vortex (ABV)
The ABV is initiated by the secondary separation line on the
leeward side of the aft ship near the hull bottom. It separates from
the hull shortly before the end of the skeg. The ABV is clearly
visible in all simulation. This is valid for the steady and averaged
unsteady simulations. The vortex follows the free steam direction
after it leaves the hull and remains visible for a long distance
behind it, see Figure 8 and Figure 9.
It can be seen in Figure 11 that over quite a range of x/Lpp the y-
coordinates of ABV core have a constant angle relative to the
centerline of the ship. This tendency is captured well by the
applied methods with the exception of the Edge-EARSM code. A
good agreement between the calculated z-coordinates and the
measured values has also been achieved for the z- coordinates;
the differences are located in the range of x/Lpp=± 0.03, see
Figure 11.
The variation of the Q-value in the vortex core along the non-
dimensional x-axis is presented in Figure 11. The results of
ReFRESCO and FreSCo+ show the same tendency that the Q
decreases over x/Lpp. The results of Edge-EARSM and Edge-
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 14
HYB0 also follow the same tendency but with reduced Q-values.
Edge-EARSM predicts the lowest Q-values. The predicted
gradient of Q by all applied methods over x/Lpp is nearly the
same.
The variation of the ωx along the non-dimensional x-axis is
presented in Figure 11. The results in the x/Lpp region higher than
0.8 show the same tendency, namely, that the vorticity decreases
over x/Lpp. Edge-EARSM predicts the lowest ωx-values. The
ABV is strongly influenced by the shear flow in the wake region
behind the ship. The measured results not only confirm the
calculated tendency, but the absolute values of the measurement
and the computations are also in good agreement. The identified
position of helical instability by Xing et al. [45] is characterized
by a strong reduction of the ωx.
Figure 11 shows the comparison of the axial velocity component.
The calculated values of FreSCo+, Edge-HYB0 and Edge-
EARSM agree with the measured values. While the ReFRESCO
results over quite a range are also in good agreement with the
measured values, CFDShip-Iowa overpredicts the axial velocity
component of the ABV over the range.
Figure 11 includes the comparison of the pressure coefficient and
the TKE, respectively. The calculated pressure coefficients by
ReFRESCO, Edge-HYB0 and FreSCo+ are in the same range,
although Edge-HYB0 predicts a much higher pressure coefficient
at or near x/Lpp=0.9. The maximum pressure coefficient by
Edge-EARSM is much lower than those by other applied
methods. The results of CFDShip-Iowa show a steep increase of
the pressure coefficient at or near x/Lpp=1.05; all other codes
predict a gradual pressure increase. The pressure level far behind
the ship hull is nearly the same in all applied methods.
Compared with CFDShip-Iowa, the calculated mean values of the
TKE by Edge-HYB0 are quite high. The ReFRESCO results do
not show any high gradient of the TKE. In contrast, computations
using anisotropic models such as CFDShip-Iowa and Edge-
HYB0 show high fluctuations. The reason for the strong
reduction of TKE calculated by CFDShip-Iowa at x/Lpp=1.1 is
not clear. The TKE predicted by CFDShip-Iowa shows an
increase at x/Lpp=1.05. At this position a high local pressure
increase is predicted by the same method, compare Figure 11. In
Figure 11, it can be seen that at x/Lpp=1.1 a reduction of ωx takes
place. All these parameters can be interpreted as an indication for
helical instability at this location.
Comparisons of global vortex characteristics between EFD and
CFD
A summary of the comparison between the EFD and the CFD
results is presented in Table 6, Table 7 and Table 8. The tables
include the percentage deviation between EFD and the CFD
regarding the coordinates of the vortex core, the longitudinal
velocity and vorticity. The results of ReFRESCO (SST 2003,
12.7M), FreSCo+ (SST k-ω 2003, 11.0M), CFDShip-Iowa (ARS-
DES, 13.0M), Edge (ERSM, 17.4M) and Edge (HYB0, 17.4M)
are compared. The estimated mean uncertainty of the measured
values is 5.5%.
For the FSV, it can be seen that the accuracy of the predicted y-
and z- coordinates is higher compared with the other values. The
deviation of the predicted longitudinal velocity and the vorticity
are high near the onset, see the results at x/Lpp=0.3153. The
overall deviation lies in the range between 13% and 27%, see
Table 8. The level of deviations is higher for the ASV and ABV
(20.8% to 42%), see Table 6, Table 7 and Table 8. The reason
may be that ABV and a considerable part of ASV are located on
the after-body of the ship, where a strong shear flow and
interaction between the different vortices take place.
Limiting Streamlines The limiting streamlines will be discussed in this section. In the
figures belonging to this section, different separation /
reattachment lines / areas are marked as followed:
SL 1 = Separation Line FBV,
SL 2-1 = Separation Line FSV, the forward part of the second separation line about 0.2L- 0.62L, on ship bottom,
SL 3-1 = Separation Line ASV, separation line close to the bilge radius,
SL 3-2 = Separation Line ASV, separation line close on the ship bottom,
RL 3 = Reattachment Line ASV,
SL 4-1 = Separation Line ABV, the after part of the second separation line about 0.62L- 0.95L, close to the bilge radius,
SL 4-2 = Separation Line ABV, the after part of the third separation line till about 0.65L- 0.95L, on leeward ship side,
RL 4 = Reattachment Line ABV, Figure 10,
SL 5 = Separation Line SV,
SA 6 = Separation Area ABHPV.
They are only marked as far as they are clearly identifiable in the
corresponding views. The numbering of the different vortices
corresponds to the numbering in Section: Vortical Structures. For
the CFD results for which a vortex core analysis is available, the
core location of this vortex is marked with a blue dashed line in
the figures (Figure 10).
Figure 7: Visualization of limiting streamlines on the wind
tunnel model bow and stern section.
These measured data of the wind tunnel oil film test are presented
in Figure 7. In the central region of the hull, unfortunately, no
0.2 0.30.1
FSV - 1
primary separation lineprimary reattachment line
SL 1SL 2-1
SL 3-1
RL 3
0.7 0.8 0.9
ASV - 1
ASV - 11
secondary separation lineprimary reattachment line
primary
separation lineASV - 6
separated flow
region
SL 5
SL 3-1
RL 3
SL 4-1 SA 6
third separation lineSL 4-2
SL 3-2
RL 4
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 15
results are present. The Figures show the limiting streamlines on
the model hull obtained by the oil film test. In order to identify
the position of the different vortical structures, the dimensionless
positions along the longitudinal axis of the model are plotted in
the figures, where 0L and 1L are the locations of the forward and
after perpendicular, respectively. Figure 7 shows at the top the
limiting streamlines on the fore-body. The locations of the FBV
and the FSV can be easily identified; the streamlines in these
areas are light grey. Dark grey indicates the flow separation area,
as the oil film keeps its position due to negligible flow speed in
this area. The dashed line shows the positions of appearance and
development of the ASV. Behind this region, the primary lines
for separation and reattachment can be identified. Figure 7 at the
bottom shows the separation area and reattachment lines on the
after-part bottom.
In order to analyze the characteristics of the flow, the measured
and calculated limiting streamlines directions on the model hull
are compared. The limiting streamlines predicted by CFD codes
can be seen in Figure 10. These pictures identify the separation
and reattachment lines. The different limiting streamlines for the
FSV, ASV and ABV will be discussed in detail in the following.
Separation Lines FSV, SL 2-1
Shortly after disappearance of the SL 1, the separation line of the
FSV (SL 2-1) starts on the ship bottom. It is the forward part of
the secondary separation line in the region between 0.2L-0.62L.
It proceeds directly on the surface of the hull in the region located
between the bilge radius and the hull bottom and ends at the after
shoulder. At the beginning of SL 2-1, the FSV separates from the
hull. On its way to the aft ship, the SL 2-1 adds energy to the FSV.
The SL 2-1 is predicted by all CFD solvers similarly and agrees
very well with the wind tunnel tests. This is not surprising since
this separation line develops at a striking geometric location on
the hull.
Separation Line ASV, SL 3-1, SL 3-2
The ASV separation consists of two separation lines (SL 3-1 and
SL 3-2), which can be clearly identified in all simulation results
(Figure 10). In the wind tunnel oil film test (Figure 7 bottom),
both the SL 3-1 and the SL 3-2 are present but are hard to identify
due to reflection on the model surface. The SL 3-1, also called
primary separation line, begins near the forward shoulder at about
0.22-0.25L and develops directly on the transition from windward
hull side to the bilge radius parallel to the chine. At the aft
shoulder (circa 0.7L), the separation line changes its direction and
follows more or less the free stream direction. It crosses the hull
and ends at 0.86L at the secondary separation line or SL 4-1,
respectively. It is predicted by all CFD results in the same manner
and fits well to the measurements. Only the starting point differs
a little bit.
The SL 3-2 lies more or less centrally between the SL 3-1 and the
reattachment line RL 3 (see next section). Its starting point is
predicted in the simulations quite differently. In the FreSCo+ and
FOI Edge (EARSM) results, it starts quite early at 0.4L and
before, whereas it appears rather late, at 0.65L, in the CFDShip-
Iowa results. The other results lie within this range. The
development is then similar to the SL 3-1 and it also ends at the
secondary separation line (SL 4-1), but a little earlier at 0.83L. In
the measurements, the SL 3-2 lies closer to the SL 3-1 than in the
numerical simulations and seems to start rather late as in the
CFDShip-Iowa results. Another small reattachment line lying
between these two separation lines can be found in all simulation
results. This complex structure of separation and reattachment
lines is due to the complex interaction between the large and small
vortex structures generated in this area. In Figure 10, where the
core location of the ASV is included, it can be seen that the ASV
lies very close to SL 3-2 and has more or less the same shape. In
the results of FreSCo+, ReFRESCO and both of FOI Edge
(EARSM and HYB0), the ASV is located on the leeward side of
SL 3-2, whereas it is on the windward side in the CFDShip-Iowa
results.
Reattachment Line ASV, RL 3
The reattachment line RL 3 starts near the front shoulder at 0.22L
on the windward side of the model and moves along the model
bottom toward to the centerline of the model. It is caused by the
ASV when its rotation ensures that the flow is again directed
orthogonal to the hull bottom and flows onto it. It ends at the
secondary separation line on the leeward side of the hull bottom
at about 0.83L. The shape of the reattachment line differs in the
numerical results. FreSCo+, CFDShip-Iowa, FOI Edge (EARSM)
and NavyFOAM predict it as a straight line, ReFRESCO also has
a straight line but with an earlier ending, whereas it has an s-shape
in the FOI Edge (HYB0) and FOI Open FOAM results, which
might be due to the different turbulence modeling. So far it is
visible in the measurements it seems to be a straight line.
Separation Line ABV, SL 4-1, SL 4-2
The separation line of the ABV (SL 4-1) is the rear part (0.62L-
0.95L) of the secondary separation line which starts at the fore-
body and extends till the end of the hull bottom along the chine.
It proceeds directly on the transition from the hull bottom to the
bilge radius and ends at the aft position of the flat bottom. The
main separation causal for the ABV takes place from 0.86L till
the end of hull bottom (0.95L). This is the part after the separation
lines of the ASV (SL 3-1 and SL 3-2) cross the secondary
separation line. However, as can be partially seen on the pictures
of the vortex structures (Figure 8), the ABV is additionally
initiated till the secondary separation line passes 0.65L, the rear
shoulder. The SL 4-1 is predicted by all CFD codes similarly and
agrees well with the wind tunnel tests. This is due to the fact that
this separation line develops at a striking geometric location on
the hull.
The SL 4-2 is the rear part of the third separation line and lies on
the leeward hull side at about 0.65L-0.95L. This separation line
does not lead to a recognizable vortex. When the third separation
line comes to the aft ship behind the rear shoulder, it moves far
away from the ship bottom due to the influence of the hull shape.
The predictions of the SL 4-2 differ among different CFD codes
(Figure 10) and are hardly identifiable in some results. The
predictions are in agreement with the wind tunnel oil film test, see
Figure 7 bottom. An exception is the result of FOI Edge
(EARSM), where the third separation line is pushed towards the
outside and the secondary reattachment line becomes clearly
visible at this place.
Reattachment Line ABV, RL 4
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 16
The RL 4 is the rear part of the secondary reattachment line. It
starts at the rear shoulder at about 0.6L but shortly after that the
location of RL 4 is hard to identify and it is hard to define where
it really ends. This is also true for the wind tunnel oil film test
results, see Figure 7 bottom. In the results of FOI Edge (EARSM)
in Figure 10, this reattachment line is clearly visible. With some
imagination it can also be found in the other CFD results.
Planar Plots A further comparison of the measured and calculated results is
given in Figure 12. The results are presented exemplary for the
section ASV-11. In each figure, the results contributed by the
different CFD codes are placed.
In general, it can be noted that the CFD results are able to capture
the main flow features seen in the experimental results. The CFD
results seem to be quite similar at first sight, but there are some
important differences in the three main different vortex regions
that will be described and discussed below.
After-Body Side Vortex (ASV)
The ASV-11 is located at x/Lpp=0.7030. The corresponding
results can be found in Figure 12. The wind tunnel measurements
in this section cover both the ASV and the FSV.
In this plane, the ASV is located nearly close to the centerline
(slightly more leeward) of the hull bottom. The distance between
the ASV center and the wall surface of the model bottom varies
among the simulation results. Additionally, the calculated
strength of the ASV shows noticeable differences. Here, the
ReFRESCO, FOI Edge (HYB0) and NavyFOAM show the
highest ωx values. The NavyFOAM results again illustrate a
multiple core vortex system, which is no longer the case in the
FreSCo+ results.
The FSV is located leeward of the hull and its distance to the hull
is the same as the previous section. The core position of the vortex
in all CFD results agrees very well with the experiment. All CFD
codes underpredict x. The FOI OpenFOAM results show the
highest and the FOI Edge (EARSM) the lowest ωx values.
Concerning the TKE data, it can be stated that the TKE values
are, in general, lower in the ReFRESCO results compared to the
FreSCo+ results. Figure 12 shows the distribution of Tut on the
leeward side of the hull. It can be seen that Tut values are high in
the boundary layer and in the ASV region. The pattern of the FSV
becomes clearly visible TKE and Tut plots.
CONCLUSION Experimental Investigation
An extensive experimental study has been conducted by the
Hamburg University of Technology (TUHH) for a detailed
validation of CFD predictions for flow over a double model of the
MOERI tanker (KVLCC2) at static drift angle of 30 degrees. The
aim of the test case is determining the most important features of
the flow on ships with high block coefficient during maneuvers.
The flow at high static drift angle is very complex and dominated
by multiple vortices of various origins emanating along the hull.
The uncertainties were estimated according to the International
Towing Tank Conference (ITTC) Recommended Procedures and
Guidelines 7.5-01-03-03 “Uncertainty Analysis – An Example
for PIV Measurement” (ITTC 2008). The estimated uncertainties
for three velocity components are Uz = ± 0.08m/s, Uy = ± 0.06m/s
and Ux = ± 0.33m/s. The relative uncertainties of the velocity
components to the free stream velocity are Uz = ± 0.30%, Uy =
±0.22% and Ux = ± 1.22%. The uncertainty of the longitudinal
vorticity ωx is calculated based on the uncertainties regarding the
velocity components and the measuring positions. The estimated
uncertainty of ωx is ±5.32 Lpp/U∞.
The uncertainty of the measured velocity component parallel to
the inflow Ut using PIV-technique is ± 0.536m/s and 1.98%
relative to the free stream velocity. The absolute and the relative
uncertainty of the measured results using LDA-techniques for the
Ut are ± 0.2m/s and: ±0.74%, respectively. The uncertainties can
be locally higher in some areas due to the reflection of the model
walls.
To capture the global flow structure, flow visualization tests were
conducted in the wind tunnel. The tests include a smoke test for
visualizing the vortical flow structure around the model and a
classic oil film method for identifying the limiting streamlines
and separation areas on the model surface.
The results show that most of the vortices are displaced far from
the hull once they are generated. Thus, the evolution of the mean
flow and turbulence in their cores tends to occur in a free shear
regime. But there are also vortices which progress close to the
hull surface and, thus, it is expected that these have strong
interactions with the boundary layer flow of the hull.
In the results of the planer velocity, the main vortices can be
clearly identified as FSV, ASV, ABV and SV. In the smoke tests,
FSV, ASV and ABV could be visualized. The results of the oil
film method in the stem and stern regions give a clear indication
for the influence of the FBV and the SV on the limiting
streamlines. In the stern region, the separation area ABHV can be
clearly seen. Due to the strong reflection of the laser beam in
certain locations, the quality of the measured results is limited,
but in general, the majority of the experimental data seem
reasonable and reliable.
The measured vorticity and axial velocity component of the FSV
show different characteristics compared with the corresponding
values of the other vortices, namely vorticity and axial velocity
component of the FSV increase downstream while these values
are nearly constant or decrease for other vortices. The increase of
the vorticity and axial velocity component of FSV may be a result
of the secondary vortex structure around the FSV. This structure
can also be noticed around the leading edge vortex of delta foil.
CFD Computations
There were 7 CFD submissions from five different institutions.
Different turbulence models were used, ranging from different k-
ω models to DES, LES modeling to various combinations of
these. In most submissions, the boundary layer on the hull was
resolved down to the surface, but also wall functions were used.
Analyses of the vortex core data were carried out for all
submissions with the exception of NavyFOAM and FOI-
OpenFOAM. The limiting streamlines, onset and separation were
analyzed for all submissions.
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 17
The resolution of the grids used by different groups ranged from
11M to 77M. NavyFOAM simulations used the finest grid,
whereas FreSCo+ simulations used the coarsest grid. The grids
used for most of the simulations were not finer than 18M, except
for those used by FOI OpenFOAM and NavyFOAM. One of the
important conclusions drawn from this study is that fine grids in
the vortices regions are mandatory to accurately capture the onset
and progression of the vortices. Numerical dissipation can
completely change the strength of the vortices and therefore the
interaction between them.
In general, a good agreement is achieved among the CFD
methods applied for the prediction of the dominant vortical
structures, but less agreement is achieved for the vortical
structures on the leeward side of the ship hull. This applies mainly
to the axial vorticity and axial velocity of the FSV, which show a
decrease in all CFD methods (an exception is the axial velocity
prediction by CFDShip-Iowa), whereas it has a constant or
increasing level in a certain range of x/LPP. Also, some methods
predict secondary vortices for the ASV vortex system. The
OpenFOAM-LES results show significant small-scale resolved
turbulent vortical structures. The separation pattern and topology
were consistent with the available experimental data.
Forces and Yaw Moment
Many of the CFD submissions include the forces and yaw
moment for different grid resolutions. Grid dependency studies
have been carried out by CFDShip-Iowa, ReFRESCO and
FreSCo+ with four, seven and three grids, respectively. The
calculated forces and yaw moment on the seven grids considered
by CFDShip-Iowa and on the three grids used by FreSCo+ are
given in Table 5. The results of ReFRESCO are given only for
the final grid. Only CFDShip-Iowa has applied quantitative
solution verification including forces (X, Y) and moment (N) on
two grid-triplet studies with a refinement ratio √2. The results of
the verification study show that a monotonic convergence is
achieved for X on (1, 2, 3), whereas oscillatory convergence is
achieved for Y on (1, 2, 3) and (2, 3, 4) and for N on (1, 2, 3). The
non-smooth grid convergence is due to different flow physics
between coarse and fine grids and the lack of solution verification
methods for DES where the numerical and modeling errors are
strongly coupled.
Table 5 shows that the X and Y forces calculated by FreSCo+ have
a monotonic convergence behavior, whereas for N shows an
oscillatory behavior.
The variation range of the computed X force by different codes is
quite large. It varies between -0.03× 10−2 and -0.581× 10−2.
Although a systematic verification study for all applied methods
is not conducted, the X-force obtained by OpenFOAM using
LES-MM is the lowest and by CFDShip-Iowa using ARS-DES is
the highest. Compared with X, the range of variation of the Y
force is limited. The lowest and the highest values are 25.2× 10−2
and 31.7× 10−2. The lowest and highest values are obtained
again by OpenFOAM-LES-MM and CFDShip-Iowa-ARS-DES,
respectively. A similar tendency can be noticed for the yaw
moment N. The lowest value 5.09 × 10−2 is obtained by
OpenFOAM-LES-MM and the highest 7.27 × 10−2 is calculated
by CFDShip-Iowa-ARS-DES.
The wide range of the calculated X force (E= -90.35% to +
86.98%) shows that this component is more sensitive to the
applied turbulence model than the Y force. The E range for Y is -
15.18% to +13.93%, and the E range for N = -21.87% to
+11.63%. The calculated force components obtained by the k-ω
model are close to each other although a large variation of the grid
resolution exists. As the Y force is less sensitive to the applied
turbulence model, the predicted yaw moment also shows less
scattering.
An overview of normalized force and yaw moment coefficients
is given in Table 5. Although extensive V&V studies are not
carried out, some comments are given on the presented results.
The ARS-DES (13M nodes) model predicts the highest and the
LES-MM (36.5M nodes) the lowest value. The results of two-
equation turbulence models, such as standard k-ω or SST k-ω,
show a decrease of the calculated X-force coefficient when
increasing the grid resolution, see Table 5.
Vortical Structures:
As shown in Figure 8, all the solvers are more or less consistent
in the prediction of vortical structures. CFDShip-Iowa,
ReFRESCO and FOI Edge predict very similar results, whereas
FreSCo+ (steady), FOI OpenFOAM and NavyFOAM predict
many secondary vortices for FSV. FOI OpenFOAM and
NavyFOAM show secondary vortices for ASV. The nature of
FSV secondary vortices predicted by FreSCo+ and FOI-
OF/NavyFOAM is different. As shown in Figure 8, the shape of
the secondary vortices calculated by FreSCo+ is completely
changed when the computation was carried out as an unsteady
case. The instantaneous shape of the secondary vortices from
FreSCo+ is very similar to the ReFRESCO results. FOI hybrid
RANS-LES model shows very low resolved turbulence levels in
instantaneous plot. It seems like HYB0 suffers from turbulence
trigger issues similar to DES, as observed in straight-ahead 5415
case. The results of FOI OpenFOAM LES show significant small-
scale resolved turbulent vortical structures.
Vortex Core Analysis:
Figure 11 show that the CFD codes predict the FSV core location
well. This is consistent with 5415 results. The FSV core x-
vorticity is underpredicted by 50% by CFD for x/L > 0.6, see
Figure 11. All CFD simulations show a similar trend. EFD also
shows an increasing trend in axial velocity for x/L between 0.7-
0.8. The increase in the core could be due to either the influence
of the secondary vortices or the interaction between the FSV and
the ASV.
The FSV x-velocity shows large errors similar to x-vorticity for
x/L > 0.6. The EFD data shows a sharp flow deceleration for x/L
between 0.7 and 0.8. Combined with the x- vorticity, there
appears to be a strong interaction between the FSV and the ASV
in the experiments, which CFD do not predict. The influence of
the secondary vortices may also play an important role in this
context.
Overall, all codes predict the FSV reasonably well in comparison
with the experiments; CFDShip-Iowa predicts most accurate core
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 18
axial velocity, i.e., longitudinal velocity component in the vortex
core increases, which is not captured by other codes; all codes
predict decreasing axial vorticity, whereas experiments showed
increasing trends.
As shown in Figures 11, y- and the z-locations of ASV are
predicted well. The z-location shows wider variation, especially
for x/L between 0.6 and 0.7. In the experiments, the vortex
sharply moves upwards around x/L = 0.7, which is not predicted
in any CFD results. This is probably due to FSV-ASV interaction,
which is missing in CFD predictions.
For the axial vorticity component ωx, CFD predictions are,
overall, in good agreement with the experiments. CFDShip-Iowa
underpredicts ωx. RANS predictions seem to be best for ωx. All
CFD underpredict experimental core axial velocity by 20-40%.
Because the ASV is much closer to the model surface than the
other vortices, the quality of the experimental results may suffer
from the wall reflection in this region.
ABV predictions using URANS are significantly better than those
for the sonar dome tip vortex (SDTV) of the combatant 5415 at β
= 20° predictions. Overall, all codes predict ABV reasonably well
in comparison with the experiments; CFDShip-Iowa and
ReFRESCO over-predict core axial velocity compared to other
codes, see Figure 11.
In general, all CFD predictions compare reasonably with EFD
data during the onset and early stage of the progression of the
vortices. However, details of the simulated flow are different
from measurements further downstream. The core coordinates of
the main vortices are predicted well by the CFD methods
considered in the vortex core analysis. The same is valid for the
axial vorticity component, with the exception of the FSV. This
vortex arises in the boundary layer of the model, leaves the
boundary layer very fast and progresses in the outer flow region.
Therefore, a considerable part of the FSV can be considered as an
isolated vortex with negligible interaction with the surrounding
outer flow and these circumferences allow the vortex to keep its
strength over a quite long distance.
Turbulence Model
From the planar solution it becomes obvious that the predictions
for the FSV and the ABV are quite similar in both URANS and
hybrid RANS/LES or LES. NavyFOAM results show multiple
vortex separations for ASV, which probably are caused by the use
of a different turbulence model with wall functions. The
applicability of the wall functions for separated flows under
adverse pressure gradients as in the case of the flows on KVLCC2
at large drift angles needs further validation.
Prediction of significant small-scale resolved turbulent structures
and reasonable mean-flow predictions by FOI-OpenFOAM with
wall-modeled LES suggests that LES simulations are reliable in
free shear regions away from the hull. Low resolved turbulence
level in FOI hybrid RANS-LES suggests that HYB0 suffers from
the turbulence trigger issue similar to DES, as observed in the
straight-ahead 5415 case.
The effect of using steady state calculations for an unsteady flow
is investigated by FreSCo+. The comparison between the steady
and unsteady calculations shows a considerable influence on the
structure of the secondary vortices around the FSV and negligible
changes of the predicted characteristics of the main vortices. The
reason for this could be caused by insufficient iterative
convergence in the steady simulation, which is four orders of
magnitude higher.
With the current grids and solvers, there does not appear to be one
turbulence model that can accurately predict all aspects of the
flow. DES underpredicts the TKE levels. The calculated
separation areas by using NavyFOAM and Edge-HYB0 are
significantly larger than the area observed in the model tests.
The results show that the numerical dissipation of vortical flows
can be a weak point in the simulations. This problem can be
mitigated by using high quality grids with a strong local
refinement in the regions of the expected main vortices. Besides
the need of accurate turbulence closure models, it may be useful
to develop numerical methods that are able to solve the
momentum conservation equations based on velocity-vorticity
formulation.
Surface Streamlines
Vortices show open-type separation and reattachment, and are
identified by converging and diverging streamlines. All solvers
agree very well for the prediction of separation lines SL 1, SL 2-
1, SL 3-1 and SL 3-2; and reattachment lines RL 3 and RL 4.
SL 5 (SV separation) is predicted well by all solvers except FOI
Edge HYB0 and FOI OpenFOAM-LES. The latter solvers show
the presence of nodes, suggesting the formation of an additional
closed-type separation, which is physically possible. FOI
OpenFOAM-LES and NavyFOAM predictions show complex
flow streamlines between RL 3, SL 3-1 and SL 3-2, related to the
separation and reattachment of ASV. This correlates with the
ASV secondary vortices predicted by the solver in Figure 8. ASV
secondary vortices could be predicted due to wall modeling used
by both FOI-LES and NavyFOAM.
FreSCo+, CFDShip-Iowa and ReFRESCO predict mostly similar
results as all use near wall modeling. FOI OpenFOAM-LES and
NavyFOAM show complex surface streamlines on after-body
windward side likely due to effects of wall functions.
Future work should also focus on:
(a) Improving the accuracy of computing the leading edge
vortex; special attention should be given to vorticity transport
and reducing the numerical dissipation,
(b) Development of numerical methods that are able to solve the
momentum conservation equations based on velocity-
vorticity formulation,
(c) Investigation of RANS-LES transition modeling for hybrid
RANS-LES calculations,
(d) Additional experimental test of the present test case for
confirmation of current EFD findings,
(e) Development of collaborative experimental programs for
generating detailed validation data, especially velocity and
turbulence fields on ship hulls in unsteady motion,
(f) Validation by using experimental data including free surface
effects, if available.
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 19
ACKNOWLEDGMENTS The U.S. Office of Naval Research under Grant N00014-10-1-
0017 sponsored the research at the University of Iowa under the
administration of Drs Thomas Fu and Ki-Han Kim. Drs Patrick
Purtell and Ki-Han Kim provided guidance to the international
collaboration over the course of this study and Dr Kim graciously
aided in editing. Dr Stephan Hitzel, Airbus, provided consultation
on the assessment of the ship-flow vortex breakdown and helical
mode instability/spiral vortices.
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Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 21
Figure 8: Predicted vortical flow structure steady/ time-averaged results, Q=100.
Figure 9: Predicted vortical flow structure, instantaneous results, Q=100.
Figure 10: Predicted limiting streamlines. Blue dashed line indicates the ASV core position.
secondary separation line
primary reattachment lineprimary separation line
RL 3SL 3-1 SL 5
SL 4-1SL 1 SA 6
SL 3-2
0.60.1 0.2 0.50.3 0.4 0.7 0.8 0.9
SL 2-1SL 1
SL 2-1
SL 3-1RL 3
SL 5SL 3-2
0.60.1 0.2 0.50.3 0.4 0.7 0.8 0.9
primary reattachment line
primary separation line
secondary separation line
SL 4-1
0.60.1 0.2 0.50.3 0.4 0.7 0.8 0.9
RL 3
SL 3-1
SL 5
SL 4-1SL 2-1
SL 1
SA 6
SL 3-1
Third SL 4-2
separationline
SL 3-2
Primary
separationline (ASV)
Primary
reattachmentline Separation
line (ABHV)
Separation
line (ABV)Secondary
separationline (FSV)
Separation
line (FBV)
0.60.1 0.2 0.50.3 0.4 0.7 0.8 0.9
primary reattachment lineprimary separation line
secondary separation line
RL 3SL 3-1 SL 5
SL 4 -1
SL 2-1
SL 1SA 6
third separation linesecondary reattachment line
SL 3-2
SL 4 -2RL 4
primary separation line
0.60.1 0.2 0.50.3 0.4 0.7 0.8 0.9
secondary separation line
primary reattachment line
RL 3SL 3-1
SL 5
SL 4-1
SL 2-1
SL 1 SA 6
third separation line
SL 3-2
SL 4-2
0.60.1 0.2 0.50.3 0.4 0.7 0.8 0.9
primary reattachment line
secondary separation line
primary separation line
RL 3SL 3-1 SL 5
SL 4-1
SL 2-1
SL 1 SA 6
SL 3-2
0.60.1 0.2 0.50.3 0.4 0.7 0.8 0.9
primary reattachment line
secondary separation line
primary separation line
RL 3 SL 3-1 SL 5
SL 4-1
SL 2-1
SL 1 SA 6
SL 3-2
CFDShip-Iowa ReFRESCO
CFDShip-Iowa
FreSCo+, steady FreSCo+, unsteady
NavyFOAM
FreSCo+
ReFRESCO
NavyFOAM
FOI Edge HYB0
FOI OpenFOAM
FOI OpenFOAM FOI Edge HYB0
FOI Edge EARSM
FOI OpenFOAM FOI Edge HYB0
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 22
Figure 11: Vortex core analyses: FSV (left), ASV (middle) and ABV (right).
0,00
0,05
0,10
0,15
0,20
0,25
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4
Co
re y
/Lp
p L
oca
tio
n
x/Lpp
Variation of FSV Ycore
inception of helical instability (CFDShip-Iowa)
inception of helical instability (FreSCo+)
-0,15
-0,10
-0,05
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4
Co
re y
/Lp
p L
oca
tio
n
x/Lpp
Variation of ASV Ycore
inception of helical instability
inception of helical instability (FreSCo+)
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,6 0,8 1,0 1,2 1,4 1,6
Co
re y
/Lp
p L
oca
tio
n
x/Lpp
Variation of ABV Ycore
inception of helical instability (CFDShip-Iowa)
inception of helical instability (FreSCo+)
-0,08
-0,07
-0,06
-0,05
-0,04
-0,03
-0,02
-0,01
0,00
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4
Co
re z
/Lp
p L
oca
tio
n
x/Lpp
Variation of FSV Zcore
inception of helical instability (CFDShip-Iowa)
inception of helical instability (FreSCo+)
-0,10
-0,09
-0,08
-0,07
-0,06
-0,05
-0,04
-0,03
-0,02
-0,01
0,00
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4C
ore
z/L
pp
Lo
cati
on
x/Lpp
Variation of ASV Zcore
inception of helical instability
(CFDShip-Iowa)
inception of helical instability (FreSCo+)
-0,08
-0,07
-0,06
-0,05
-0,04
-0,03
-0,02
-0,01
0,00
0,6 0,8 1,0 1,2 1,4 1,6
Co
re z
/Lp
p L
oca
tio
n
x/Lpp
Variation of ABV Zcore
inception of helical instability (CFDShip-Iowa)
inception of helical instability (FreSCo+)
10
100
1000
10000
100000
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4
Q
x/Lpp
Variation of FSV QPeak
inception of helical instability (FreSCo+)
10
100
1000
10000
100000
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4
Q
x/Lpp
Variation of ASV QPeak
inception of helical instability (FreSCo+)
10
100
1000
10000
100000
0,6 0,8 1,0 1,2 1,4 1,6
Q
x/Lpp
Variation of ABV QPeak
inception of helical instability (FreSCo+)
0
100
200
300
400
500
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4
Co
re A
xial
Vo
rtic
ity
x/Lpp
Variation of FSV ωx,core
inception of helical instability (CFDShip-Iowa)
inception of helical instability (FreSCo+)
0
100
200
300
400
500
600
700
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4
Co
re A
xial
Vo
rtic
ity
x/Lpp
Variation of ASV ωx,core
inception of helical instability (CFDShip-
Iowa)
inception of helical instability (FreSCo+)
-100
0
100
200
300
400
500
600
0,6 0,8 1,0 1,2 1,4 1,6C
ore
Axi
al V
ort
icit
y
x/Lpp
Variation of ABV ωx,core
inception of helical instability (CFDShip-Iowa)
inception of helical instability (FreSCo+)
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4
Co
re A
xial
Ve
loci
ty
x/Lpp
Variation of FSV Ux,core
inception of helical instability (CFDShip-Iowa)
inception of helical instability (FreSCo+)
0,0
0,2
0,4
0,6
0,8
1,0
1,2
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4
Co
re A
xial
Ve
loci
ty
x/Lpp
Variation of ASV Ux,core
inception of helical instability
(CFDShip-Iowa)
inception of helical instability (FreSCo+)
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
1,8
0,6 0,8 1,0 1,2 1,4 1,6
Co
re A
xial
Ve
loci
ty
x/Lpp
Variation of ABV Ux,core
inception of helical instability (CFDShip-Iowa)
inception of helical instability (FreSCo+)
-1,8
-1,6
-1,4
-1,2
-1,0
-0,8
-0,6
-0,4
-0,2
0,0
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4
Co
re P
ress
ure
x/Lpp
Variation of FSV cpcore
inception of helical instability (CFDShip-Iowa)
inception of helical instability (FreSCo+)
-1,6
-1,4
-1,2
-1,0
-0,8
-0,6
-0,4
-0,2
0,0
0,2
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4
Co
re P
ress
ure
x/Lpp
Variation of ASV cpcore
inception of helical instability
(CFDShip-Iowa)inception of helical instability (FreSCo+)
-1,8
-1,6
-1,4
-1,2
-1,0
-0,8
-0,6
-0,4
-0,2
0,0
0,6 0,8 1,0 1,2 1,4 1,6
Co
re P
ress
ure
x/Lpp
Variation of ABV cpcore
inception of helical instability (CFDShip-Iowa)
inception of helical instability (FreSCo+)
0,000
0,005
0,010
0,015
0,020
0,025
0,030
0,035
0,040
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4
Co
re T
KE
x/Lpp
Variation of FSV TKEcore
inception of helical instability (CFDShip-Iowa)
inception of helical instability (FreSCo+)
0,000
0,005
0,010
0,015
0,020
0,025
0,030
0,035
0,040
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4
Co
re T
KE
x/Lpp
Variation of ASV TKEcore
inception of helical instability
(CFDShip-Iowa)
inception of helical instability (FreSCo+)
0,000
0,005
0,010
0,015
0,020
0,025
0,030
0,035
0,040
0,045
0,6 0,8 1,0 1,2 1,4 1,6
Co
re T
KE
x/Lpp
Variation of ABV TKEcore
inception of helical instability (CFDShip-Iowa)
inception of helical instability (FreSCo+)
0,00
0,10
0,20
0,30
0,40
0,50
0,60
0,70
0,80
-0,6 1,4
Co
re y
/Lp
p L
oca
tio
n
x/Lpp
ReFRESCO, 12.7M, SST2003 FreSCo+, 11.0M, SST k-ω 2003 FreSCo+, ω based identification CFDShip-Iowa, 13.0M, ARS-DES
EFD, PIV Edge, 17.4M, EARSM Edge, 17.4M, HYB0
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 23
Figure 12: Planar plots ASV-region section 11, : 𝑈𝑥, 𝑈𝑦 , 𝑈𝑧, 𝜔𝑥, 𝑇𝑈𝑡 and TKE.
𝑈𝑥
𝑈𝑦
𝑈𝑧
𝜔𝑥
𝑇𝑈𝑡, TKE
EFD: TUHH
EFD: TUHH
EFD: TUHH
EFD: TUHH
EFD: TUHH
FreSCo+
FreSCo+
FreSCo+
FreSCo+
FreSCo+
ReFRESCO
ReFRESCO
ReFRESCO
ReFRESCO
ReFRESCO
CFDShip-Iowa
CFDShip-Iowa
CFDShip-Iowa
CFDShip-Iowa
OpenFOAM
OpenFOAM
OpenFOAM
OpenFOAM
NavyFOAM
NavyFOAM
NavyFOAM
NavyFOAM
Edge, EARSM
Edge, EARSM
Edge, EARSM
Edge, EARSM
Edge, EARSM Edge, HYB0
Edge, HYB0
Edge, HYB0
Edge, HYB0
Edge, HYB0
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 24
Table 3: Main characteristics of the CFD codes
Organization / code
name
Modeling Grid characteristics
Turbulence Wall boundary
Steady
/unsteady
calculation
Type/Size Resolution
Iowa Institute of Hydraulic Research of the University of Iowa (IIHR) CFDShip-Iowa
EARSM
DES
low Re near wall
turbulence model,
no slip condition
unsteady
overset,
multiblock
structured;
0.6M,1.6M,
4.6M and 12.9
M points
grid refinement
block around the
ship hull
Maritime Research Institute Netherlands (MARIN) ReFRESCO
k- SST
(1994 and
2003
versions)
low Re near wall
turbulence model,
no slip condition
steady
structured
0.12M, 1.59M,
2.27M, 3.34M,
5.38M, 8.45M
and 12.72M
multiblock
structured O–O
Hamburg University of Technology (TUHH) FreSCo+
k- SST
(2003)
low Re near wall
turbulence model,
no slip condition
steady /
unsteady
unstructured
2.97M, 4.15M
and 11M
grid refinement
around the ship
hull and in the
wake area
Swedish Defence Research Agency (FOI) Edge RANS-Simulation
EARSM in
combination
with
Hellsten k-ω
low Re near wall
turbulence model,
no slip condition
unsteady unstructured,
17.4M
grid refinement
around the ship
hull and in the
wake area
Swedish Defence Research Agency (FOI) Edge RANS-LES-Simulation
RANS-LES
HYB0, algebraic
mixing-length in
combination with
the SGS model by
Smagorinsky
(1963).
unsteady unstructured,
17.4M
grid refinement
around the ship
hull and in the
wake area
Swedish Defence Research Agency (FOI) OpenFOAM
LES, Mixed
Model
LES boundary-
layer equations unsteady
unstructured,
36.5M
grid refinement
around the ship
hull and in the
wake area
aval Surface Warfare Center Carderock Division (NSWCCD) NavyFOAM
k- model
(Wilcox,
2008)
wall function
condition
y+ = 40-100
steady unstructured
grid, 77M
grid refinement
around the ship
hull and in the
wake area
Table 4: Overview of generated grids for all CFD solvers.
IIHR
CFDShip-
Iowa
Grid 1 2 3 4
Ship 144×88×35=
443,520
203×122×49=
1,213,534
287×174×69=
3,445,722
406×244×98=
9,708,272
Background 76×47×41=
146,452
107×66×58=
409,596
152×93×82=
1,159,152
214×132×116=
3,276,768
Total 589,972 1,623,130 4,604,874 12,985,040
y+ (max.) 1.13 0.80 0.56 0.40
MARIN
ReFRESCO
Grid 1 2 3 4 5 6 7
Number
of cells 121,330 1,590,144 2269674 3,340,098 5,388,408 8,454,880 12,721,152
Elements
on hull 2904 17216 21978 27740 38904 52528 68864
y+ (max.) 2.82 1.45 1.29 1.13 1.01 0.86 0.74
TUHH
FreSCo+
Grid 1 2 3
Number of cells 2.97 M 4.15 M 11.0 M.
Typical cell size in
refinement area (mm) 5.0 × 5.0 × 5.0 3.54 × 3.54 × 3.54 2.5 × 2.5× 2.5
y+ (max.) 1.2 1.2 1.2
FOI
Edge
Grid 1
Number of nodes 17.4 M
Number of elements 73.5 M
Elements on hull 524408
y+ (mean, URANS + hyb0) 0.49
FOI
OpenFOAM
Grid 1
Number of nodes 36.5 M
Number of elements 202.0 M
Elements on hull 611403
y+ (mean) 10.7
NSWCCD
NavyFOAM
Grid 1
Number of cells 77 M
y+ (90% of all values) 40-100
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 25
Table 5: Overview of normalized force coefficients for the different
calculations. Only light blue marked computations are considered for
RMS value calculation.
Solver Grid size
in M.
Turbulence model
Steady / unsteady
calculation
X' [-] ×10-2
E% RMS
Y’ [-] ×10-2
E% RMS
N’ [-] ×10-2
E% RMS
RMS value of all
highlighted CFD results
- - - -0.311 - 27.836 - 6.515 -
CFDShip-Iowa (IIHR)
0.59 ARS-DES unsteady -0.481 54.79 32.736 17.61 7.418 13.87
1.6 ARS-DES unsteady -0.614 97.60 31.325 12.54 7.142 9.63
4.6 ARS-DES unsteady -0.629 102.42 32.096 15.31 7.202 10.55
13.0 ARS-DES unsteady -0.581 86.98 31.713 13.93 7.272 11.63
ReFRESCO (MARIN)
12.7 SST1994 steady -0.154 -50.44 26.023 -6.51 5.488 -15.76
12.7 SST2003 steady -0.063 -79.73 25.695 -7.69 5.552 -14.78
FreSCo+
(TUHH)
2.97 standard
k-ω steady -0.094 -69.75 26.698 -4.09 6.866 5.39
4.15 standard
k-ω steady -0.088 -71.68 26.691 -4.11 6.789 4.21
11 standard
k-ω steady -0.079 -74.58 26.275 -5.61 6.883 5.65
2.97 SST k-ω
2003 steady -0.159 -48.83 27.988 0.55 6.817 4.64
4.15 SST k-ω
2003 steady -0.143 -53.98 27.562 -0.98 6.745 3.54
11 SST k-ω
2003 steady -0.134 -56.88 27.533 -1.09 6.818 4.66
11 SST k-ω
2003 unsteady -0.131 -41.16 27.416 2.91 6.884 11.19
Edge (FOI) 17.4 EARSM unsteady -0.518 -75.22 24.83 -15.18 5.457 -9.28
17.4 HYB0 unsteady -0.234 -24.69 23.92 -14.07 5.508 -15.45
OpenFOAM (FOI)
36.5 LES-MM unsteady -0.03 -90.35 25.2 -9.47 5.09 -21.87
NavyFOAM (NSWCCD)
77 Wilcox’ k-
model steady -0.166 -46.58 28.1 0.95 6.09 -6.52
Table 6: Axial vortex core prediction errors for FSV.
Vortex CFD Vortex
location x/Lpp
Flow variable prediction error, ABS (E%D)
Overall USN UD UV
y/Lpp z/Lpp Ux/U 𝝎x*Lpp
/U
FSV
ReFRESCO, 12.7M,
SST2003
0.3765 3.3 2.2 4.8 35.4 11.4
5.5
0.4326 3.6 0.7 14.5 9.7 7.1
0.4866 0.6 1.0 20.0 13.1 8.7
0.7029 6.4 17.0 39.0 54.7 29.3
0.7472 7.3 15.4 36.0 66.5 31.3
AVG 4,3 7,3 22,9 35,9 17,6
FreSCo+, 11.0M, SST k-ω 2003
0.3765 4.1 4.1 0.2 57.0 16.4
5.5
0.4326 4.2 1.1 6.5 25.7 9.4
0.4866 0.8 0.9 14.8 4.5 5.3
0.7029 5.2 17.9 28.4 56.2 26.9
AVG 3,6 6,0 12,5 35,8 14,5
CFDShip-Iowa,
13.0M, ARS-DES
0.3765 9.1 1.3 0.5 1.3 3.0
5.5
0.4326 9.5 2.4 3.3 33.8 12.2
0.4866 5.3 11.0 4.3 41.0 15.4
0.6840 3.2 2.9 10.1 70.7 21.7
0.7029 2.7 3.3 8.9 74.8 22.4
0.7316 5.1 1.6 3.3
0.7472 3.9 2.7 3.3
AVG 5,5 3,6 5,4 44,3 11,6
Edge, 17.4M, EARSM
0.3765 3.7 5.4 18.5 20.8 12.1
5.5
0.4326 3.6 5.2 22.1 33.1 16.0
0.4866 0.4 6.5 27.2 47.5 20.4
0.6840 7.8 3.3 38.1 64.7 28.5
0.7029 6.9 9.1 39.3 69.4 31.2
0.7316 8.7 5.6 37.1 74.8 31.6
0.7472 7.6 5.9 36.2 78.3 32.0
AVG 5,5 5,9 31,2 55,5 24,5
Edge, 17.4M, HYB0
0.3765 1.7 5.9 9.6 10.6 7.0
5.5
0.4326 2.6 2.6 13.5 7.3 6.5
0.4866 0.4 5.3 20.5 25.3 12.9
0.6840 8.6 4.1 33.6 46.7 23.2
0.7029 8.2 10.3 35.5 53.3 26.8
0.7316 10.6 6.9 33.2 60.1 27.7
0.7472 9.9 6.7 33.5 67.6 29.4
AVG 6,0 6,0 25,6 38,7 19,1
Abdel-Maksoud Experimental and Numerical Investigations of the KVLCC2 at 30° Drift Angle 26
Table 7: Axial vortex core prediction errors for ASV.
Vortex CFD
Vortex location
x/Lpp
Flow variable prediction error, ABS (E%D)
Overall USN UD UV
y/Lpp z/Lpp Ux/U 𝝎x*Lpp/
U
ASV
ReFRESCO, 12.7M,
SST2003
0.5309 95.3 0.2 12.6 102.5 52.7
5.5
0.5818 18.9 3.7 28.4 7.0 14.5
0.6156 2.0 0.1 30.3 29.0 15.4
0.7472 41.1 18.3 28.2 225.1 78.2
AVG 39.3 5.6 24.9 90.9 40.2
FreSCo+, 11.0M, SST k-ω 2003
0.5309 52.1 6.7 12.1 54.2 31.3
5.5 0.5818 32.4 1.8 24.2 19.0 19.4
0.6156 6.1 8.7 30.8 1.1 11.7
AVG 30.2 5.8 22.4 24.8 20.8
CFDShip-Iowa,
13.0M, ARS-DES
0.5309 161.5 6.1 46.8 64.8 69.8
5.5
0.5648 27.1 4.0 43.7 49.6 31.1
0.5818 1.7 12.6 38.5 60.4 28.3
0.6156 40.3 9.7 29.0 43.3 30.6
0.6326 88.9 17.9 23.9 32.1 40.7
0.6495 67.1 18.2 26.6 40.8 38.2
0.6840 136.8 17.6 25.4 53.2 58.3
0.7166 63.6 11.4 9.7 60.0 36.1
0.7472 51.0 14.7 16.6 32.6 28.7
AVG 70.9 12.5 28.9 48.5 40.2
Edge, 17.4M, EARSM
0.5309 66.4 1.2 24.4 32.5 31.1
5.5
0.5648 12.3 2.5 34.7 23.0 18.2
0.5818 24.9 5.8 33.5 35.8 25.0
0.6156 1.9 3.5 25.6 15.7 11.7
0.6326 11.3 5.3 19.6 0.2 9.1
0.6495 40.7 7.7 21.3 6.1 19.0
0.6840 25.2 9.8 21.8 17.7 18.6
0.7166 40.4 23.0 11.6 17.2 23.0
0.7472 29.4 21.9 23.7 62.8 34.4
AVG 28.1 9.0 24.0 23.4 21.1
Edge, 17.4M, HYB0
0.5309 79.9 1.7 19.2 157.8 64.6
5.5
0.5648 3.3 1.5 24.9 167.5 49.3
0.5818 26.7 7.5 33.9 9.3 19.4
0.6156 11.9 1.9 39.8 23.5 19.3
0.6326 1.7 12.7 39.6 42.6 24.2
0.6495 18.0 14.0 41.2 26.6 25.0
0.6840 47.8 12.7 35.4 15.4 27.8
0.7166 38.1 14.1 24.4 29.7 26.6
0.7472 28.5 15.3 38.1 168.7 62.6
AVG 28.4 9.0 32.9 71.2 35.4
Table 8: Axial vortex core prediction errors for ABV.
Vortex CFD Vortex
location x/Lpp
Flow variable prediction error, ABS (E%D)
Overall USN UD UV
y/Lpp z/Lpp Ux/U 𝝎x*Lpp/
U
ABV
ReFRESCO, 12.7M,
SST2003
0.9368 16.9 1.1 48.6 198.8 66.4
5.5
1.0345 3.9 9.5 60.9 43.0 29.3
1.2332 15.2 10.0 2.7 8.4 9.1
1.3303 16.1 8.8 2.5 16.8 11.1
1.4241 9.4 2.0 8.0 16.9 9.1
1.5362 8.9 20.6 19.4 10.8 14.9
AVG 11.7 8.7 23.7 49.1 23.3
FreSCo+, 11.0M, SST k-ω 2003
0.9368 19.8 2.7 4.1 164.9 47.9
5.5
1.0345 6.9 11.0 10.6 17.1 11.4
1.2332 9.7 21.6 14.8 25.7 18.0
1.3303 5.9 31.9 13.0 17.7 17.1
1.4241 1.3 20.5 0.5 31.0 13.3
1.5362 2.9 13.0 10.8 64.5 22.8
AVG 7.8 16.8 9.0 53.5 21.7
CFDShip-Iowa,
13.0M, ARS-DES
0.9368 45.5 6.2 98.2 243.9 98.4
5.5
1.0345 23.6 16.0 72.3 11.0 30.7
1.2332 21.3 8.6 29.9 100.4 40.0
1.3303 19.1 7.7 30.9 96.5 38.5
1.4241 12.2 22.6 17.4
1.5362 14.9 38.5 26.7
AVG 22.8 16.6 57.8 112.9 42.0
Edge, 17.4M, EARSM
0.9368 16.9 4.0 15.5 81.8 29.5
5.5
1.0345 3.8 17.4 19.2 35.1 18.9
1.2332 12.2 4.7 7.2 50.0 18.5
1.3303 10.7 11.9 6.7 38.7 17.0
AVG 10.9 9.5 12.2 51.4 21.0
Edge, 17.4M, HYB0
0.9368 8.3 1.2 59.0 151.4 55.0
5.5
1.0345 1.2 16.1 45.5 2.5 16.3
1.2332 20.3 19.5 4.3 23.4 16.9
1.3303 22.3 3.2 2.4 8.1 9.0
AVG 13.1 10.0 27.8 46.3 24.3