# Assessment of statistical and hybrid LES turbulence closures for surface combatant DTMB5415 at 20° static drift condition

Michel Visonneau, Emmanuel Guilmineau, Jeroen Wackers, Ganbo Deng, Patrick Queutey

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Michel Visonneau, Emmanuel Guilmineau, Jeroen Wackers, Ganbo Deng, Patrick Queutey. Assessment of statistical and hybrid LES turbulence closures for surface combatant DTMB5415 at 20° static drift condition. 34th International Conference on Ocean, Offshore and Artic Engineering (OMAE 2015), May 2015, St. John's, Canada. 10.1115/OMAE2015-41372. hal-01202568

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ASSESSMENT OF STATISTICAL AND HYBRID LES TURBULENCE CLOSURES
FOR SURFACE COMBATANT DTMB5415 AT 20° STATIC DRIFT CONDITION

Michel Visonneau

Emmanuel Guilmineau

Jeroen Wackers

GanBo Deng

Patrick Queutey

LHEEA, CNRS UMR 6598

Ecole Centrale de Nantes, 1 rue de la Noë

BP 9210 44321 Nantes Cedex 3, France

ABSTRACT

This paper provides detailed validation of the complex free-surface flow around the surface combatant DTMB5415 at 20° static drift conditions. Particular emphasis is being placed on the onset and progression of the various vortical structures created at the sonar dome, at the free-surface and around bilge keels in conditions where free-surface breaking may occur. A detailed analysis of this complex free-surface flow is conducted on grids which are dynamically refined to capture the vortical structures. Local comparisons with recent experiments performed at the Iowa Institute of Hydraulic Research (IIHR) during a joint NATO-AVT (Advanced Vehicle Technologies) collaboration are used to perform detailed flow analysis and draw some conclusions about the actual potentialities of advanced Computation Fluid Dynamics (CFD) method in terms of physical and numerical modeling.

INTRODUCTION

The simulation of the onset and progression of longitudinal vortices is a major challenge in ship hydrodynamics because the accurate prediction of the flow in the core of vortices during their progression is strongly affected by numerical and turbulence modeling errors. This is however a topic of great practical importance since elongated bodies like ships give rise to various longitudinal vortices emanating from bulbous bows, sonar domes, hull-struts junctions, for instance. The accurate prediction

of these flow structures and their trajectories can be crucial
for global force prediction but also for the design of propellers
when they interact with the propeller disk.

During the Gothenburg 2010 workshop, the calm water straight-ahead condition was studied in [1]. The low Froude number $Fr = 0.142$ large block coefficient $C_b = 0.81$ tanker hull forms (KVLCC2) and the higher $Fr$ smaller $C_b = 0.51$ surface combatant DTMB5415 were chosen as test cases and used to assess in great detail the respective influence of discretization and modeling errors on the generation and progression of longitudinal vortices. For the KVLCC2, it was established that statistical anisotropic turbulence closures were still the best models to predict the generation of longitudinal vortices occuring in the aft part of the ship through the progressive thickening of the boundary layer. Hybrid Large-Eddy Simulation (LES) approaches, because of unphysical management of the turbulence production between the Reynolds-Averaged Navier-Stokes Equations (RANSE) domain and the pure LES region, were not able to generate enough turbulence in the LES region, leading to much too intense longitudinal vortices.

For the DTMB 5415, it appeared that the onset of vortical structures was highly dependent on the local grid fineness around the sonar dome. Actually, with a very fine grid built with the help of an automatic grid refinement (AGR) procedure, it was possible to predict the onset of all the vortical structures visible in detailed experiments without any significant influence of the turbulence
closures. However, once generated, the progression of these lon-
gitudinal structures was found to be highly dependent on the tur-
bulence closures, even if a sufficiently fine grid was kept in the
core of the vortices, thanks to the AGR procedure used with
ad-hoc criterion. None of the above-mentioned closures (i.e.
anisotropic statistical turbulence closures or DES model (also
called hybrid LES closure)) were fully satisfactory, the statisti-
cal closures creating too much turbulence viscosity while DES
did not generate enough turbulence in the core of the vortices.
The reader can refer to [2] for more details on this topic.

The work presented in this study was performed during a col-
laborative project with NATO and partner countries under the
auspices of the NATO AVT-183 Reliable Prediction of Separated
Flow and Onset and Progression for Air and Sea Vehicles. The
objective of this collaborative study is to present a first assess-
ment of the DTMB5415 for the 20° static drift condition, includ-
ing analysis of the turbulence modeling, grid resolution and onset
and progression of vortex structures. Some of the salient results
will be provided in this paper.

EXPERIMENTAL MODEL AND DATA

The experimental data used herein for 5415 with bilge keels at Fr=0.28 at static drift 20° condition is comprised of resistance and moments, wave elevation and profiles, flow and vorticity contours at several planes along the hull and isosurfaces of vorticity or velocity-gradient tensor invariant at selected 3D volumes along the primary vortices ( [3], [4], [5]). The hull form used in the tests was the DTMB 5512, a 1:46.6 scale, 3.048 m long model, which is a geosym of the DTMB 5415, a 1:24.8 scale, 5.72 m model. The full-scale hull form is a preliminary design for a surface combatant for the US Navy. Characteristic features of the DTMB 5415 hull include a transom stern and a sonar dome bow. The model was un-appended except for bilge-keels, i.e., not equipped with shafts, struts, propellers, nor rudders (see Figure 1). The ship model was tested at three static drift angles β = 0°, 10° and 20°, at a Fr = 0.28. This Froude number corresponds to the full-scale cruising speed of the vessel at 20 knots, and corresponds to 1.53 m/s for model scale. The model was fixed at its dynamic sinkage σ = 1.92 10⁻³Lₚₚ and trim = 0.136° (bow down). Here Lₚₚ is the length between perpendiculars. The tests were conducted in calm-water conditions.

CFD: THE ISIS-CFD FLOW SOLVER

The solver ISIS-CFD, available as a part of the
FINE™/Marine computing suite, is an incompressible unsteady
Reynolds-Averaged Navier-Stokes (URANS) solver mainly de-
voted to marine hydrodynamics. The discretization is based on
a fully unstructured face-based finite volume method to build
the spatial discretization of the transport equations. Pressure-

<figure><img src="image_2.png" /><figcaption>FIGURE 1. DTMB5415 MODEL</figcaption></figure>

velocity coupling is enforced through a Rhie & Chow SIM-
PLE type method: at each time step, the velocity updates come
from the momentum equations and the pressure is given by the
mass conservation law, transformed into a pressure equation.
The method features several sophisticated turbulence models:
apart from the classical two-equation k − ε and k − ω models,
the anisotropic two-equation Explicit Algebraic Stress Model
(EASM), as well as Reynolds Stress Transport Models, are avail-
able [6, 7] with or without rotation corrections. All models are
available with wall-function or low-Reynolds near wall formula-
tions. Hybrid LES turbulence models based on Detached Eddy
Simulation (DES and variants) are also implemented and are val-
idated on automotive flows characterized by large separations
(see [8]). Additionally, several cavitation models are available in
the code. Free-surface flow is simulated with a multi-phase flow
approach: the water surface is captured with a conservation equa-
tion for the volume fraction of water, discretized with specific
compressive discretization schemes [9]. Finally, a parallelized
anisotropic automatic grid refinement procedure has been devel-
oped which is controlled by various flow-related criteria [10].

RESULTS AT 20° DRIFT ANGLE

Settings

Two unstructured grids have been generated with
HEXPRESS™ without taking into account the presence of
the tank walls. The first one, called here G1, is comprised of
27 million nodes while the second one is dynamically refined
during the computations with the AGR procedure included in
ISIS-CFD. This grid called G2 comprises only 10 million nodes.
The automatic grid refinement used to create it is based on an
hybrid criterion blending a free-surface and a vortex capturing
criteria built with the regularized Hessian of the pressure. The
minimum cell size is set at 2 mm for a ship length of 3.048m.
Although these grids are still too coarse to capture accurately
the progression of all the longitudinal vortices generated at the
sonar dome and behind the breaking wave, along the entire
hull and below the free-surface, these simulations can be used
with confidence to assess the need in terms of discretisation
and turbulence modeling in the vicinity of their region of onset.
Figures 2 and 3 compare the grid density between G1 and G2 at
two cross-sections in the fore region. Directional and anisotropic
adaptation is noticeable at the first section, Figure 2, associated
with strong air/water interface deformations due to the high
drift condition. In that section refinement has been created also
at the vicinity of the sonar dome surface to be correlated with
the presence of high pressure gradients. In the second section,
Figure 3, a significant vortical structure on starboard side has
developed which is illustrated by a localised region of refined
grid with smaller cell sizes than provided with the fine grid.

<figure><img src="image_3.png" /><figcaption>(a) FINE (G1)</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>(b) AGR (G2)</figcaption></figure>

<caption>FIGURE 2. GRID TOPOLOGY AT $X/L_{PP}=0.06$</caption>

Three different turbulence models are used, $k-\omega$ SST, EARSM and DES-SST, for the computations performed on grid G1. For the grid G2 built with AGR, only the $k-\omega$ SST model has been employed.

## Forces

The agreement on the forces and moments shown in Tab. 1 is quite satisfactory for all the turbulence models and grids used. For the resistance, the best agreement is obtained with $k-\omega$ SST on the grid built with AGR with a comparison error of -0.35%D while the worst result is given by EARSM on the fine grid with a comparison error of 5.17%D. For the lateral force, the best agreement is reached by DES-SST on grid G1 with a comparison error

<figure><img src="image_5.png" /><figcaption>(a) FINE (G1)</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>(b) AGR (G2)</figcaption></figure>

<caption>FIGURE 3. GRID TOPOLOGY AT $X/L_{PP}=0.20$</caption>

of -0.22%D while the maximum error is 4.16%D for $k-\omega$ SST on grid G2. Finally, for the moment N, the best agreement with the measured value is provided by $k-\omega$ SST on grid G2 with a maximum error of -1.93%D obtained with the model EARSM on grid G1.

## Wave elevations

Figure 4 shows the mean wave elevations for URANSE and DES-SST results on the grids G1 and G2. The wave patterns are globally very similar. An asymmetric wave elevation distribution is observed where two waves are generated from the bow, with angle 10° from the windward side (portside) and 40° from the leeward side (starboard). A strong breaking wave, with a large wave trough reaching the vicinity of the sonar dome, can be noticed on the leeward side (see figure 5). This wave trough is unsteady with a periodic growth and shrinkage of moderate amplitude, which means that the wave trough never disappears. This free-surface unsteadiness leads to a periodic temporal evolution of the wall streamlines below the free-surface close to this location. A second weaker shoulder wave can also be observed on the leeward side. On the windward side, a relatively weaker diverging wave emanates from the bow beginning with a wave crest.
<table><caption>TABLE 1. COMPARISONS OF FORCES BETWEEN CFD AND EFD. E%D=(S-D)/D*100</caption><thead><tr><th>Case</th><th>X×10<sup>-3</sup> - E%D</th><th>Y×10<sup>-3</sup> - E%D</th><th>N×10<sup>-3</sup> - E%D</th></tr></thead><tbody><tr><td>EFD</td><td>-28.57</td><td>153.57</td><td>59.86</td></tr><tr><td>URANS+AGR, k-ω SST (G2 - 10M)</td><td>-28.47 - -0.35</td><td>159.95 - 4.16</td><td>59.97 - 0.18</td></tr><tr><td>URANS, k-ω SST (G1 - 27M)</td><td>-29.01 - 1.54</td><td>155.68 - 1.38</td><td>58.91 - -1.58</td></tr><tr><td>URANS, EARSM (G1 - 27M)</td><td>-30.05 - 5.17</td><td>154.98 - 0.92</td><td>58.71 - -1.93</td></tr><tr><td>DES (G1 - 27M)</td><td>-28.06 - -0.35</td><td>153.24 - -0.22</td><td>60.88 - 1.70</td></tr></tbody></table>

<figure><img src="image_7.png" /><figcaption>FIGURE 4. EFD AND CFD WAVE CONTOURS</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**FIGURE 5.** INSTANTANEOUS VIEW OF THE BREAKING WAVE ON THE LEEWARD SIDE</figcaption></figure>

The simulated and measured wave profiles at $y_{ship} = -0.222$ on portside and $y_{ship} = 0.212$ on starboard side are shown in figures 6. The global agreement is quite satisfactory, considering the complexity of the wave profiles. A slight influence of the turbulence model and local grid density on the free-surface elevations can be noticed but it is difficult to draw any reliable conclusions on the basis of these fragmented comparisons.

<figure><img src="image_9.png" /><figcaption>**FIGURE 6.** EFD AND CFD WAVE PROFILES</figcaption></figure>

## Mean vortical structures

During the NATO/AVT joint collaboration, IIHR proposed a classification of mean vortex structures observed in this configuration by drawing the iso-surfaces Q=50 colored by the helicity. This terminology is retained in the present paper and shown in Figure 7(a). For a drift angle of 20°, the free-surface deformation is very large and leads to wave breaking and ventilation phenomena which are accompanied by the generation of two intense free-surface vortices (FSV) on the windward and leeward sides. These vortices, named by IIHR, LW-FSV and WW-FSV, originate from $x/L_{PP} = 0.013$ and progress towards the free-surface where they are associated with significant free-surface deformation. LW-FSV appears more intense and extends up to $x/L_{PP} = 0.190$ while WW-FSV extends up to $x/L_{PP} = 0.217$. From the sonar dome, three different vortices can be observed. The first and more intense one emanates from the leeward side of the sonar dome and is called Sonar Dome Tip Vortex (SDTV) by IIHR. Its extension varies according to the turbulence models (up to $x/L_{PP} = 1.677$ for EARSM and $x/L_{PP} = 1.744$ for DES-SST). An additional vortex, named Leeward ForeBody Keel Vortex (FBKV-LW), counter rotating to SDTV, is generated at the extremity of the sonar dome keel while its counterpart named WindWard ForeBody Keel Vortex (FBKV-WW), co-rotating with SDTV, is also visible in all the computations performed with every turbulence model on grids G1 or G2. The extension of these two vortices is more limited (up to $x/L_{PP} = 0.431$) where they are probably erased by the numerical diffusion. The analysis of the flow on the leeward side of the bow of the ship is far more complex. We notice the existence of a region of separated flow which is slightly unsteady because of the strong interactions of the separated flow with an unsteady breaking wave. The surface streamlines indicate the presence of a spiral point, whatever the turbulence closure used (see Figure 8). From these spiraling wall streamlines emerges a strong helical vortex convected below the free surface. This vortical structure is unsteady, periodically growing and shrinking in time and correlated with a similar unsteadiness of the leeward breaking wave. Around the bilge keels on the leeward side, two to three vortices are also visible starting from the leading edge, the middle part and the trailing edge of the leeward bilge keel. Their intensity is moderate like their spatial extension. They are all called bilge keel vortices (BKV). From the windward side, far more intense vortices (called BKTV vortices) are generated at the windward bilge keel. It seems that we can distinguish two such BKTV vortices, one of them having a large spatial extension since it moves below the hull and interacts up to $x/L_{PP}=1.690$.

## Onset and progression analysis of SDTV

Figures 10 show the longitudinal evolution of several physical variables in the SDTV vortex cores. To identify the vortex cores, we have launched a streamline from the onset point identi-
<figure><img src="image_10.png" /><figcaption>FIGURE 7. ISO-SURFACES OF Q=50 COLORED BY RELATIVE HELICITY</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>FIGURE 8. INSTANTANEOUS WALL STREAMLINES TOPOL-
OGY ON THE LEEWARD SIDE OF THE SONAR DOME</figcaption></figure>

fied with great care and have recorded the longitudinal evolution
of these variables at several locations along this line. This ex-
plains why we have data in the region where the SDTV vortex is
no more detected by the iso-surface Q=50. However, this does
not mean that the vortex has been completely diffused here but,
rather, that its intensity is weaker, leading to Q value positive but
smaller than 50. This was checked by drawing the secondary
velocities in a plane normal to the vortex line, confirming the
existence of a transverse rotational motion. Figures 10 showing
Q<sub>peak</sub> and axial vorticity ω<sub>x</sub> confirm that the intensity of SDTV
is strongly under-predicted, whatever turbulence closures used.
For instance, ω<sub>x</sub> is twice less intense in the computations than in
the experiments, which points out the lack of grid points in this
specific region. The prediction of ω<sub>y</sub> and ω<sub>z</sub> is somewhat better,
whatever turbulence closures used. The trajectory of SDTV is re-
markably well predicted since we can observe an almost perfect
agreement between computations and measurements of Y and Z
evolutions along the SDTV vortex core. The evolution of the
longitudinal velocity component Ux is better predicted with the
AGR 10M points grid and is somewhat under-predicted on the
27M points grid, underlining again the role played by the local
discretization error for this kind of flow. The turbulent kinetic en-

ergy (TKE) appears also to be strongly under-predicted in every
computation.

Planar Variables

EFD data are available for comparisons with CFD at x/LPP =0.06, 0.1, 0.12, 0.2, 0.4, 0.6, 0.8, 0.935 and 1.0. Data concerns axial velocity, cross flow streamlines, vorticity and TKE contours. For the sake of brevity, only planes 0.06 and 0.20 are shown and discussed in this paper. At x/LPP=0.06, Figure 11 for vorticity component and Figure 12 for TKE, the flow is predicted similarly by URANSE and DES-SST computations. However, but not shown here, it is interesting to mention that DES-SST is the only model able to exhibit a significant amount of TKE from x/LPP=0.02 to x/LPP=0.035, coming exclusively from the resolved part of the turbulence. This resolved turbulence may come from the turbulence locally created by the impact of the breaking wave. This hypothesis will be studied further to provide an explanation of the large disagreement between the predicted and measured turbulence kinetic energy in the core of SDTV. This resolved TKE is very quickly diffused and is hardly detected at the first experimental cross section x/LPP=0.06, Figure 12.

At x/Lpp=0.20, we can follow the progression of the most
significant vortex, the so-called sonar-dome tip vortex (SDTV).
In addition, we can notice the birth of an additional vortex close
to the hull (probably FBKV-LW) The main source of disagree-
ment between CFD and EFD concerns the level of TKE in the
core of SDTV. All the predictions on fine grid G1 fail to capture
the right amount of TKE while the computations on AGR grid G2
show a better trend. It is quite interesting to notice that DES-SST
computed on G1 does not bring any significant improvement for
this configuration.

In conclusion, before $x/L_{PP}=0.10$, the grid density seems to
be high enough to capture the relevant physics in the flow do-
<figure><img src="image_12.png" /><figcaption>FIGURE 9. EFD CFD LOCATION OF THE SDTV CORE VORTEX</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>FIGURE 10. EFD AND CFD VARIABLES IN SDTV CORE VORTEX</figcaption></figure>

main. However, the grid is probably too coarse to capture the gradients and temporal scales of a flow associated with an unsteady free-surface breaking wave on the leeward side. All turbulence closures provide very similar predictions in the flow domain and the differences are observed only on the free-surface shape, depending on the extent of the air cavity in the predicted breaking wave. After $x/L_{PP}=0.10$, the grids used in this study appear too coarse as it is suggested by the large difference observed between results on G1(fine) and G2(AGR). It seems that after this section, a major source of error comes from the discretization since the turbulence closures provide very similar results on the same grid G1, which can not be considered as ridiculously coarse. However, it is noteworthy to look at the level of TKE measured at this section. It seems that SDTV emanates from a region where a large production of TKE takes place. This high level of TKE present in the core of the vortex is then convected in the flow domain without being significantly reduced. Measurement at $x/L_{PP}=0.06$ points out also a high level of TKE approximately in the region where SDTV comes to life. This region is very close to the highly deformed free-surface characterized by a strong breaking wave and large air-cavity. It is possible that the source of this high level of TKE has to be found in the interactions between the flow and the free-surface, where a strong

production of turbulence might first take place, the turbulence being convected in the core of the SDTV vortex if the grid is fine enough. A second hypothesis would be that the SDTV vortex is not perfectly steady but changes its position in time. The large velocity fluctuations associated with this unsteadiness might be interpreted as an additional source of TKE in the PIV experiments, while they should be attributed to fluctuations in position of the core of the vortex. Another source of error might be attributed to a partial air ventilation and subsequent convection of bubbles of air inside the core of this vortex, which may disturb the measurements.

Anyway, this would plead in favor of a very fine grid free-surface capturing LES computation able to capture spatial and temporal scales associated with the free-surface and also velocity fluctuations associated with the impact of breaking waves to explain the source of this high level of TKE. Therefore, to understand the real physics, it seems necessary (i) to recheck with great care these local measurements, (ii) to use a DES-SST model to resolve as much as possible the velocity fluctuations coming from the impact of the breaking wave and make the distinction between the resolved macro-fluctuations of the velocity and the modeled turbulence, (iii) to use a locally very fine grid in order to reduce as much as possible the numerical dissipation during the progression
sion of these vortices.

## CONCLUSIONS

This paper was devoted to global and local comparisons of the free-surface flow around the DTMB5415 at 20° steady drift condition. Detailed experiments were performed at IIHR and made available in the framework of the NATO/AVT183 collaboration. Two grids with and without automatic grid refinement and several statistical and hybrid LES turbulence closures, were used and compared. The global quantities like forces and moments are satisfactorily simulated and the simulated free-surface deformation is also in good agreement with the measurements. However, more experimental information would be necessary to understand the detailed dynamics of the wave-breaking occuring on both sides of the bow. The agreement on the onset and progression of the longitudinal vortices emananting from both sides of the sonar dome and from the breaking waves is only qualitative. Obviously, these computations on grids G1, and to a lesser extent for grid G2, suffer from too large a numerical dissipation, although the improvements brought by the AGR procedure were shown. The main vortical structures visible in the three-dimensional experiments can be detected, sometimes with a good quantitative agreement. Surprisingly, the trajectories of the core of the two studied vortices SDTV and BKTV (not shown here), are in excellent agreement with IIHR measurements. However, the flow field in the core of these vortices, in terms of mean flow and turbulence, appears to be strongly damped, which makes impossible a reliable analysis of the modeling errors. An additional study with a far more refined mesh using the local automatic grid refinement functionalities implemented in ISIS-CFD should be pursued to clarify the respective predictive qualities of RANSE models versus hybrid LES closures.

## ACKNOWLEDGMENT

Recent unpublished experiments performed by IIHR in the framework of the NATO/AVT183 collaboration have been used in this paper. Professor Frederick Stern and his team are gratefully acknowledged for this very helpful initiative.

The computations were performed using HPC resources from GENCI (Grand Equipement National de Calcul Intensif) (Grant2014-0129 and Grant2014-21308), which is gratefully acknowledged.

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<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /><figcaption>**FIGURE 11.** CONTOURS OF AXIAL VORTICITY COMPONENT AT $X/L_{PP} = 0.06$</figcaption></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /><figcaption>**FIGURE 12.** CONTOURS OF TKE AT $X/L_{PP} = 0.06$</figcaption></figure>
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<figure><img src="image_25.png" /><figcaption>**FIGURE 13.** CONTOURS OF AXIAL VORTICITY COMPONENT AT $X/L_{PP} = 0.20$</figcaption></figure>

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<figure><img src="image_29.png" /><figcaption>**FIGURE 14.** CONTOURS OF TKE AT $X/L_{PP} = 0.20$</figcaption></figure>