Journal ArticleDOI

# Detailed analysis of the flow within the boundary layer and wake of a full-scale ship

15 Dec 2020-Ocean Engineering (Pergamon)-Vol. 218, pp 108022

Abstract: This article presents a detailed numerical flow assessment of the boundary layer and wake of a full-scale cargo ship. The assessment was conducted using a sophisticated numerical approach that is able to resolve large turbulent scale vortices contained in the flow. The physical flow features of the boundary layer and wake investigated include mean-velocity, near-wall shear stress and vorticity fields. Also, the evolution of the wake from the thick boundary layer over the stern is displayed and analysed in the highest possible detail. Additionally, the detailed information extracted from the boundary layer and wake was the primary input to assess the overall hydrodynamic efficiency of the full-scale general cargo ship. The analysis method followed during this work has been a determinant factor for fast and efficient design of energy saving devices, propellers or rudders that work within the limits of the boundary layer of a ship. In particular, this thorough analysis avoided the necessity to use the commonly used practice of trial and error that is typically followed in the maritime industry.
Topics: Boundary layer (61%), Wake (54%), Turbulence (51%), Vortex (50%)

## Summary (3 min read)

### 1. Introduction

• Experimental fluid dynamics towing tank tests have been traditionally used to evaluate the flow around the ship.
• Also, the aft boundary layer is significantly different in model and full-scale.
• LES resolves turbulent vortices everywhere in the flow domain down to the grid size.
• This method is more computationally affordable in ship hydrodynamics than LES, allowing the study of complex unsteady flows in full-scale and being deemed as the best alternative to calculate wake parameters, especially behind high block coefficient ships (Larsson et al., 2015).
• The authors established that both DES approaches improve the prediction of the total resistance and velocity distribution for most of the propeller plane; however, the authors also revealed that both models showed issues predicting the shear stress in the boundary layer region.

### 2. Benchmark Case Study

• The 'Regal' is a 138m single screw vessel with the following main particulars (Table 1):.
• Before the sea trials, the vessel was dry-docked, the hull was cleaned, and the propeller surface was polished.
• The scanned geometry was directly imported into the CFD computations, thus ensuring high accuracy of the geometry CAD models.
• The sea trials were conducted in a reasonably calm condition, in compliance with the ISO 15016:2015 standard (ISO, 2015) and recommended sea trails procedure ITTC 7.5-04-01-01.1 (ITTC, 2014b).
• These numerical study simulations of the flow around the ship were conducted using the commercial CFD code Siemens Star CCM+.

### 3. Numerical Approach

• This work uses the Improved Delayed Detached Eddy Simulation turbulence modelling strategy and following the approach described in previous work (Pena et al., 2019; Pena et al., 2020).
• In general, this model switches between the RANS SST k-ω model, which has demonstrated maturity and reliability calculating skin friction coefficients and steady flow features (Wilcox, 1993; Menter, 1994); and LES in away from the wall, where it can capture the larger unsteady eddies such as the bilge vortex.
• 𝐿𝐿𝐸𝑆 = 𝐶𝐷𝐸𝑆∆, being 𝐶𝐷𝐸𝑆 = 0.78, and ∆ is the grid length scale.
• This approach follows the ITTC recommended practices (ITTC, 2014c, Lloyds Register, 2016).
• The DFBI (Dynamic Fluid Body Interaction) module was used to simulate the motion of the ship in response to pressure and shear forces exerted by the fluid on the solid body, as well as gravity.

### 4. Boundary Layer Analysis Approach

• As mentioned in the introduction section, this analysis required a higher definition of the boundary layer of the ship that is required to measure the velocity profiles across the 3D ship boundary layer of the.
• All planes are parallel to each other, and their normal component is parallel to the ship length vector.
• Transversal waterline (WLi) and length planes (LGi) are also defined for reference purposes.
• Note that FR½ corresponds to the propeller plane, where nominal wake velocity measurements are taken.
• Additional probe points are installed at the flat bottom which are built through the intersection of LGi planes, FRi planes and the hull surface.

### 5. Ship Resistance: Calculated Components

• The bare hull total resistance, viscous resistance and pressure resistance are determined from the converged IDDES simulations.
• The drag forces are made dimensionless and represented by the total resistance coefficient (𝐶𝑇), pressure resistance coefficient (𝐶𝑃) and the viscous resistance coefficient (𝐶𝑉).
• Note that 𝐶𝑉 is calculated using the shear stress tensor and accounts for viscous stresses that the fluid exerts to the hull.
• Ship resistance distribution per unit length is also measured to quantify the drag contribution of each hull segment (i.e. bow, stern).
• Resistance per unit length was plotted, where 1 is at the Aft Perpendicular and 14 is at the Forward Perpendicular (F.P).

### 6. Computational Set-up

• 6.1 Time-step and Spatial Discretization The Courant number (Cr) is used to represent the number of cells that the fluid travels through within a time step, and it is defined as Cr= 𝑢∆𝑡 ∆𝑥 (where 𝑢 is the local speed, ∆𝑡 the interval of time (time step) and ∆𝑥 the cell size in the direction of the flow).
• All simulations used a 2nd order spatial and temporal discretisation for all equations.
• A very high-density mesh was generally defined in regions around the stern of the vessel , including the rudder.
• Besides, a second- order spatial resolution scheme was used to discretise the free-surface, with a trimmed mesh aligned with the calm water free-surface.
• With regards to the near-wall cell, the grid was set-up to achieve a mean y+ of 1 and ensuring that no wall functions are applied in the near-wall region.

### 7. Mesh Performance Analysis

• A mesh independence study was conducted for the simulation set-up on four different grid resolutions by varying the mesh size input parameter while holding all other parameters constant and following recommended practices (ITTC, 2017).
• The uniform parameter refinement ratio was established as √2.
• Also, mesh convergence is monitored by plotting the resolved Turbulent Kinetic Energy (TKE) convergence for the four grids at FR1 as shown in Figure 8.
• The comparison demonstrates that as desired, the core of the bilge vortex falls in the LES region and confirms that the present grid will resolve most of the vortex turbulence.
• Looking back at Figure 11, it could be seen that the LES region is already close to the near-wall region, so it could be risky to significantly reduce the mesh size, since there could be an incursion of the LES region into the RANS region and thus trigger the undesired MSD phenomenon.

### 8. Results Analysis

• The numerical results of the flow around the hull are shown and discussed in terms of ship resistance coefficients, limiting streamlines, nominal wake and the boundary layer at the stern of the ship.
• Overall, the pressure resistance displays a significant pressure imbalance between the aft and bow ends of the ship.
• Downstream at FR7 , the boundary layer considerably thickens, and stronger crossflows appear.
• The FR10 plot and WL1 series represent the velocity profiles measured on the probe point located at the intersection of the frame 'FR10' and the waterline 'WL1' (or the point PFR10WL1).
• The side vortex sheet is formed due to the change in curvature of the hull and is found to be weak when compared to the bilge vortex.

### 8. Discussion and Conclusions

• The present research has numerically investigated the ship hydrodynamic performance of a full-scale general cargo ship using extensive flow data on the boundary layer and wake field.
• This negative pressure gradient, together with the bilge vortex create the perfect environment for a local flow recirculation region near the propeller hub.
• As the flow advances, the near-wall region flow particles retard to a point where it can no longer counteract the pressure gradient, thus separating from the surface.
• The detriment on the ship efficiency is triggered by the loss of momentum that takes place on the aft end boundary layer.
• In general, the analysis conducted within this work has demonstrated to be essential to a full understanding and explanation of the underlying physical structure of the full-scale aft end flow.

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1
Detailed Analysis of the Flow Within the Boundary Layer and
Wake of a Full-Scale Ship
Blanca Pena, Ema Muk-Pavic, Patrick Fitzsimmons
Department of Mechanical Engineering, University College London, London WC1E 7JE, UK
Abstract: This article presents a detailed numerical flow assessment of the boundary layer and wake
of a full-scale cargo ship. The assessment was conducted using a sophisticated numerical approach
that is able to resolve large turbulent scale vortices contained in the flow. The physical flow features
of the boundary layer and wake investigated include mean-velocity, near-wall shear stress and
vorticity fields. Also, the evolution of the wake from the thick boundary layer over the stern is
displayed and analysed in the highest possible detail. Additionally, the detailed information extracted
from the boundary layer and wake was the primary input to assess the overall hydrodynamic
efficiency of the full-scale general cargo ship.
The analysis method followed during this work has been a determinant factor for fast and efficient
design of energy saving devices, propellers or rudders that work within the limits of the boundary
layer of a ship. In particular, this thorough analysis avoided the necessity to use the commonly used
practice of trial and error that is typically followed in the maritime industry.
Keywords: hydrodynamics, turbulent boundary layer, CFD, full scale, ship efficiency.
1. Introduction
Experimental fluid dynamics towing tank tests have been traditionally used to evaluate the flow
around the ship. The main principle of this technique is to test a scaled model of the ship in similar
conditions to that of a full scale one. This approach is expensive, time-consuming and most
importantly carries significant limitations. Among them, due to Reynolds number differences, the full-
scale boundary layer is generally thinner than in model scale. Also, the aft boundary layer is
significantly different in model and full-scale. For applications such as ship resistance investigations,
model to full-scale scaling limitations are usually overcome by the application of empirical correlation
factors (Larsson and Raven, 2010). This is not the case for boundary layer investigations where a
model to full-scale correlation approach is not yet fully established (ITTC, 2014, ITTC, 2017).
An example of model scale assessments of the boundary layer and wake was conducted by Patel et al.
(1990). This type of investigation has been beneficial to a better understanding of the flow behaviour

2
on the ship aft end. Nevertheless, when an accurate picture of the full-scale aft end flow is required, a
model scale investigation is not the most suitable option.
An alternative method to assess the near-wall flow of the ship relies on viscous flow Computational
Fluid Dynamics (CFD). It is based on the Navier-Stokes equations and allows numerical modelling of
scenarios in full-scale, therefore avoiding scaling issues. For full-scale ship hydrodynamic
applications, Reynolds Averaged NavierStokes (RANS) is known to provide a quick solution as it
does not require significant computational power. Full-scale self-propulsion studies revealed that
RANS numerical model is able to provide good quality predictions of the propeller forces and
moment (Ponkratov and Zegos, 2015; Jasak et al., 2019; Bakica et al., 2020). These investigations are
in line with the results of the Lloyds Register First Full-scale Ship Hydrodynamics Workshop (Lloyds
Register, 2016). However, RANS might not be recommended for scenarios when the flow is
predominantly unsteady and/or hull flow separation is expected, this is particularly important for
calculations of the bilge vortex that typically forms at the stern of high block coefficient ships (ITTC,
2014).
If flow separation is expected, one could consider the implementation of Large Eddy Simulation
(LES) to model the turbulence contained in the flow. The principle of LES is to approach the
modelling of turbulence by considering that the large vortical structures created by the geometry
contain most of the energy within the bulk flow. LES resolves turbulent vortices everywhere in the
flow domain down to the grid size. LES could provide more accurate predictions of the fluid flow
than RANS; however, LES is still computationally unaffordable in full-scale ship hydrodynamics due
to the high Reynolds number.
A most recent approach for the simulation of turbulent ship flows is based on a combination of
RANS/LES, such as DES (Detached Eddy Simulation). This method combines the best features of
LES and RANS by only using LES away from the wall where a high level of unsteadiness of the flow
is expected (i.e. around the bilges, detached flow regions or in the wake) while RANS is applied in the
near-wall region. This method is more computationally affordable in ship hydrodynamics than LES,
allowing the study of complex unsteady flows in full-scale and being deemed as the best alternative to
calculate wake parameters, especially behind high block coefficient ships (Larsson et al., 2015). Full-
scale flow predictions using a DES97 and its improved version, a DDES, were conducted by Xing et
al. (2010). The authors established that both DES approaches improve the prediction of the total
resistance and velocity distribution for most of the propeller plane; however, the authors also revealed
that both models showed issues predicting the shear stress in the boundary layer region. Some of these
issues might be attributed to the log-layer mismatch behaviour that the DES97 and DDES models
exhibit (Spalart et al., 2006) which could be corrected using an IDDES approach and which represents
an improved version of the DDES and DES97 approaches (Shur et al., 2008a).

3
This paper presents a thorough analysis of the aft end boundary layer and wake of a full-scale ship.
The numerical approach used during this analysis is based on an IDDES approach that was previously
validated against sea trials torque data (Pena et al., 2020). Also, the computational mesh was tailored
to allow for the resolution of the largest turbulent vortex that is expected to be shed from the hull: the
bilge vortex. Nominal wake, resistance distribution and velocity fields have been post-processed to
assess the hydrodynamic performance of the 'MV Regal' (Lloyds Register, 2016), a full-scale general
cargo ship.
2. Benchmark Case Study
The 'Regal' is a 138m single screw vessel (Figure 1) with the following main particulars (Table 1):
Table 1 Regal main particulars (Lloyds Register, 2016)
Parameter
Length between perpendiculars, Lpp
138 m
Breadth moulded, B
23 m
Depth moulded, D
12.1 m
Draught, T
Ballast
Propeller diameter, D
5.2 m (four-bladed)
Before the sea trials, the vessel was dry-docked, the hull was cleaned, and the propeller surface was
polished. In this clean condition, the hull, rudder and propeller were 3D laser scanned to obtain an
accurate geometric representation. The scanned geometry was directly imported into the CFD
computations, thus ensuring high accuracy of the geometry CAD models.
Figure 1 Regal general cargo ship (Lloyds Register, 2016)

4
The sea trials were conducted in a reasonably calm condition, in compliance with the ISO 15016:2015
standard (ISO, 2015) and recommended sea trails procedure ITTC 7.5-04-01-01.1 (ITTC, 2014b). The
speed trials were conducted at ballast draught at three different shaft speeds.
Therefore, the scope of the analysis corresponds to the programme conducted during the Lloyds
Register full-scale Hydrodynamics workshop. These numerical study simulations of the flow around
the ship were conducted using the commercial CFD code Siemens Star CCM+. The numerical
experiments were undertaken for the full-scale ship Regal at the ballast draft and in a clean hull
condition for the bare hull simulations (with rudder only) at the range of speeds given in Table 2. This
set of simulations significantly reduces the complexity of the aft end flow (compared with self-
propulsion tests), allowing to study the nominal wake fields.
Table 2 Bare-hull simulation conditions
Speed (knots)
Re
Fr
8
6.43E+08
0.11
10
8.03E+08
0.14
12
9.64E+08
0.17
14
1.12E+09
0.20
3. Numerical Approach
3.1 Turbulence Modelling Strategy
This work uses the Improved Delayed Detached Eddy Simulation (IDDES) turbulence modelling
strategy and following the approach described in previous work (Pena et al., 2019; Pena et al., 2020).
The IDDES belongs to the DES family, and it is based on the model developed by Shur et al. (2008).
In general, this model switches between the RANS SST k-ω model, which has demonstrated maturity
and reliability calculating skin friction coefficients and steady flow features (Wilcox, 1993; Menter,
1994); and LES in away from the wall, where it can capture the larger unsteady eddies such as the
bilge vortex. This approach ensures that attached regions are modelled by RANS whereas the
immediate region in front of the propeller (which contains the unsteady bilge vortex) is solved by
LES; ensuring that the aftermost region turbulence is better predicted than by using pure RANS.
The IDDES approach is obtained by modifying the dissipation term of the transport equation for the
turbulent kinetic energy (k). After introducing a length scale, L
hybrid
, the turbulence model equations in
tensor form are given as (Shur et al, 2008).:

5
󰇛

󰇜


󰇛
󰇜





(1)
󰇛

󰇜


󰇛
󰇜






󰇛
󰇜





(2)
where

represents the strain tensor,

the stress tensor,
is the blending function. The length
scale, L
hybrid
is defined as:

󰇛
󰇜

󰇛
󰇜


(3)
where

󰇛
󰇜
,
is given in k-Omega Model Coefficients taken as 0.09.


,
being

, and  is the grid length scale. The elevating-function
prevents an excessive
reduction of the RANS Reynolds Stresses (Shur et al., 2008b). The key of this model is the empirical
blending-function,
, which presents a switching function from RANS (
) to LES model (
).
3.2 Numerical Model of the Ship
The ship model was placed in a prismatic fluid domain with the inlet boundary placed one length
upstream of the ship's bow, the outlet boundary two ship lengths downstream of the transom of the
ship and the sides of the fluid domain one ship length towards the port and the starboard sides as
shown in Figure 6 (left). This approach follows the ITTC recommended practices (ITTC, 2014c,
Lloyds Register, 2016). A Dirichlet condition was imposed on the inlet. The DFBI (Dynamic Fluid
Body Interaction) module was used to simulate the motion of the ship in response to pressure and
shear forces exerted by the fluid on the solid body, as well as gravity. The ship model is allowed to
sink and trim freely. The resultant force and moment acting on the ship are calculated, and the
governing equations of rigid body motion are solved every time step to find the new position of the
ship. This approach was selected as it allows for direct comparison of the CFD computation integral
forces with benchmark data from the 2016 Workshop in Ship Hydrodynamics (Lloyds Register,
2016).
The properties of the ship that are defined in the simulation (Table 3) correspond to the values
determined during the sea trials (Lloyds Register, 2016).

##### Citations
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Journal ArticleDOI
Blanca Pena1, Luofeng Huang1Institutions (1)
Abstract: Ship operations are accompanied by turbulent regimes that play a significant role in the hydrodynamic characteristics. With the ongoing development of computational technologies, it is now feasible to numerically simulate turbulent ship flows with a high degree of detail. Turbulent simulations, however, tend to be computationally expensive and require a trade off between computational costs and fidelity. Whilst a range of turbulence modelling strategies is available in Computational Fluid Dynamics, there is a lack of up-to-date recommendations on their suitability for different ship-flow simulation scenarios. Addressing this gap, the present work reviews the state-of-the-art of turbulence modelling for ship hydrodynamic applications. As a result, this paper introduces the most known turbulence modelling approaches used in the field, followed by a thorough discussion of their applicabilities and limitations. Furthermore, this paper provides recommendations for the selection of turbulence modelling strategies versus various ship simulation scenarios, such as resistance prediction, ship flow modelling, self-propulsion, and cavitation analyses. It is expected that the present paper will provide decision-making support by helping CFD users minimise the time spent on trial and error, as well as providing valuable insights to promote the advancement of turbulence modelling.

##### References
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Journal ArticleDOI
Florian R. Menter1Institutions (1)
Abstract: Two new two-equation eddy-viscosity turbulence models will be presented. They combine different elements of existing models that are considered superior to their alternatives. The first model, referred to as the baseline (BSL) model, utilizes the original k-ω model of Wilcox in the inner region of the boundary layer and switches to the standard k-e model in the outer region and in free shear flows. It has a performance similar to the Wilcox model, but avoids that model's strong freestream sensitivity

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Abstract: Keywords: ecoulement : compressible Note: + disquette Reference Record created on 2005-11-18, modified on 2016-08-08

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Jinhee Jeong1, Fazle Hussain1Institutions (1)
Abstract: Considerable confusion surrounds the longstanding question of what constitutes a vortex, especially in a turbulent flow. This question, frequently misunderstood as academic, has recently acquired particular significance since coherent structures (CS) in turbulent flows are now commonly regarded as vortices. An objective definition of a vortex should permit the use of vortex dynamics concepts to educe CS, to explain formation and evolutionary dynamics of CS, to explore the role of CS in turbulence phenomena, and to develop viable turbulence models and control strategies for turbulence phenomena. We propose a definition of a vortex in an incompressible flow in terms of the eigenvalues of the symmetric tensor ${\bm {\cal S}}^2 + {\bm \Omega}^2$ are respectively the symmetric and antisymmetric parts of the velocity gradient tensor ${\bm \Delta}{\bm u}$. This definition captures the pressure minimum in a plane perpendicular to the vortex axis at high Reynolds numbers, and also accurately defines vortex cores at low Reynolds numbers, unlike a pressure-minimum criterion. We compare our definition with prior schemes/definitions using exact and numerical solutions of the Euler and Navier–Stokes equations for a variety of laminar and turbulent flows. In contrast to definitions based on the positive second invariant of ${\bm \Delta}{\bm u}$ or the complex eigenvalues of ${\bm \Delta}{\bm u}$, our definition accurately identifies the vortex core in flows where the vortex geometry is intuitively clear.

5,223 citations

01 Jan 1997

2,368 citations

Journal ArticleDOI
Abstract: Detached-eddy simulation (DES) is well understood in thin boundary layers, with the turbulence model in its Reynolds-averaged Navier–Stokes (RANS) mode and flattened grid cells, and in regions of massive separation, with the turbulence model in its large-eddy simulation (LES) mode and grid cells close to isotropic. However its initial formulation, denoted DES97 from here on, can exhibit an incorrect behavior in thick boundary layers and shallow separation regions. This behavior begins when the grid spacing parallel to the wall Δ∥ becomes less than the boundary-layer thickness δ, either through grid refinement or boundary-layer thickening. The grid spacing is then fine enough for the DES length scale to follow the LES branch (and therefore lower the eddy viscosity below the RANS level), but resolved Reynolds stresses deriving from velocity fluctuations (“LES content”) have not replaced the modeled Reynolds stresses. LES content may be lacking because the resolution is not fine enough to fully support it, and/or because of delays in its generation by instabilities. The depleted stresses reduce the skin friction, which can lead to premature separation.

1,788 citations

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