ESD design for a validation bulk carrier

Abstract

The FP7 project GRIP deals with Energy Saving Devices (ESDs). These are devices placed in front, or aft of the propeller with the aim to reduce the fuel consumption of the vessel. VICUS has worked on a hydrodynamic design procedure and had the opportunity to apply it to a validation vessel: a new-build handymax Bulk carrier by Uljanik shipyard in Croatia. VICUS has selected a downstream device, named Rudder Bulb, for this application case: it is positioned aft of the propeller and allows for a reduction of the rotational energy of the outflow. Two other partners within GRIP have also been developing their own methodology for the hydrodynamic design of an ESD. MARIN have worked on a Pre-Duct and HSVA on a Pre-Swirl Stator. Each partner has designed its ESD according to its own procedure for the Uljanik bulk carrier. From these three ESD, a cross check was carried out in order to select the device that will be manufactured on the full scale vessel. HSVA’s Pre-Swirl Stator was chosen and was been installed on the ULJ vessel. Full scale trials were carried out on the vessel, giving satisfactory results (see (Xing-Kaeding ISP (2015)) and (Hasselaar and Xing-Kaeding, ISP (2015))). In this paper, only the procedures employed by VICUS for the Rudder Bulb design as well as the results of the cross check are presented.

Keywords

Energy saving device ESD pre-swirl stator PSS pre-duct rudder bulb CFD RANS-BEM coupling frozen rotor sliding interface full scale model scale hub vortex cavitation reduction parametric model

1. Introduction

Naval architects and designers are always looking for ship improvements in order to reduce fuel consumption of a vessel and its impact on the environment. The FP7 project GRIP (Green Retrofitting through Improved Propulsion) focused on the propulsion of the vessel, with the aim to investigate devices, Energy Saving Devices (ESDs), which can be retrofitted to the stern of the vessel in order to improve the propeller efficiency and by this, reduce the required propulsion power. ESDs have been analysed and classified in different categories such as downstream devices (aft of the propeller) and upstream devices (in front of the propeller). A methodology for the ESD design has been developed by three partners: HSVA, MARIN and VICUS. Each partner used its own methodology and tools for the individual ESD designs. Finally, each partner tested its own procedure on some application cases. In this paper, we will focus on one particular application case: the Uljanik bulk carrier. This vessel is a new build handy-max bulk carrier, manufactured by partner Uljanik shipyard and it will be used as validation vessel for the ESD design. It is a unique opportunity to validate the ESD design procedure as well as the numerical tools used for the ESD design. VICUS selected a downstream device for the validation case: Rudder Bulb. MARIN chose a Pre-Duct and HSVA, a Pre-Swirl Stator. In this paper, the ESD design methodology and computational methods employed by VICUS are presented as well as the comparison of the different ESDs using VICUS tools and procedures.

2. Computational method

This section describes the computational method used by VICUS for the ESD design evaluation. RANS method software was employed by VICUS.

The numerical simulations were carried out with the computational fluid dynamic software STAR-CCM+, which is a Reynolds Averaged Navier Stokes Equations based solver. This software delivers the entire engineering simulation process in a single integrated environment. It is a software that includes the latest physical models and solver technology such as innovative meshing, model setup iterative design studies, turbulence models, transition models, cavitation, six degree of freedom motion, among others. STAR-CCM+ is a general purpose code which can handle complex geometries and complex physics. The code has several turbulence-closure models available and discretisation schemes, and they are used dependent upon the physical problem required to be solved.

The code is described focussing on incompressible flows. STAR-CCM+ solves RANSE equations in their integral form, by means of Finite Volumes methods, along with a turbulence-closure model. The spatial discretisation of convection terms is achieved by a second-order upwind scheme which is applied to both the momentum and turbulence transport properties. The diffusion terms are a central-difference and they are second-order accurate. The flow equations can be solved in coupled or in a segregated manner. The segregated flow model solves the flow equations (one for each component of velocity, and one for pressure) in a segregated, or uncoupled, manner. The linkage between the momentum and continuity equations is achieved with a predictor-corrector approach. The complete formulation can be described as using a collocated variable arrangement (as opposed to staggered) and a Rhie-and-Chow-type pressure-velocity coupling combined with a SIMPLE-type algorithm. The numerical solution is done by an aggregative algebraic multi-grid (AAMG) solver that is bases on Gauss-Seidel type of iteration technique. A fixed F-cycle method for pressure and a flexible cycle methods for momentum, and turbulent transport equations are chosen for multi-grid cycling procedure. The values of under-relaxation factors are typical. Further details about the code can be found in [3] and about numerical aspects in [1]. The rotation of the propeller is modelled using a moving reference frame system, i.e. the velocity is set on the propeller blades and centripetal effects are included in additional source terms in the momentum equations.

STAR-CCM+ provides an automatic route from complex CAD to CFD mesh. An advanced automatic meshing technology generates either polyhedral or predominantly hexahedral control volumes, offering a combination of speed, control, and accuracy. For problems involving multiple frames of reference it can automatically create conformal meshes across multiple physical domains.

In addition, it can automatically produce a high-quality extrusion layer mesh on all walls in the domain, allowing to control the position, size, growth-rate, and number of cell layers in the extrusion-layer mesh.

Finally, CAD modeller is highlighted since it allows to store an imported geometry as a CAD model, which can subsequently be converting to geometry parts for integration with the meshing and simulation process.

3. ESD hydrodynamic design and optimisation procedure

The design and optimisation procedure by VICUS is divided in five steps, as it is described in Fig. 1. The main steps conducted are as follows:

RANS computation on two different meshes (medium and fine meshes) of bare hull

ESD type selection

RANS optimisation by parametric analysis of several variables for each ESD selected

RANS computations of possible ESD combination

ESD final selection

Fig. 1.

General design and optimisation procedure chart by VICUS.

This is the VICUS general procedure to ESD design, although some steps were shifted for the Uljanik bulk carrier design. Basically, this is due to short period of time to carry out the whole procedure with the available CPU and license resources and the fact that the post-swirl device was previously selected. This will be resumed in the application of this procedure to Uljanik bulk carrier.

Each step will be explained in more detail in the following sections.

3.1. Actual ship geometry analysis

RANS resistance and self-propulsion computations of bare hull are basically performed at first stage for two reasons:

To have a basic idea of how the flow is in the area where the ESD will be located and determine its potential viability to save energy. For this first approach, the finer mesh is used to have more detail of the flow structures. It is well known that the presence of the propeller hub cap is responsible for the formation of a strong low pressure core in its centre. The low pressure of the core causes thrust deduction by pulling the propeller hub cap. Associated to this low pressure core, a vortex, named ‘hub vortex’, is shed from the end of hub cap travelling downstream of the propeller towards the rudder (Fig. 2), and therefore it yields rotational energy losses, which have to be diminished to increase the propulsive efficiency of the vessel.

Fig. 2.

Hub vortex shed from hub cap end for bare hull.

To have a base case with which compare the results of new ESD designs and to quantify the energy savings. The way to quantify the energy savings will be explained in Section 3.3: RANS optimisation.

Resistance and self-propulsion computations are carried out in model scale using frozen rotor approach for the propeller motion (if exists) and double body approach with two different meshes: medium mesh and fine mesh. The finer mesh is used to assess the figures and the flow analysis and the other one is to use during the parametric analysis.

3.2. ESD type selection

According to the vessel type and designer experience, a first ESD selection is performed to reduce the number of ESD types to study. The choice can be done between pre or post-swirls or even a combination of both. As explained previously, a rudder bulb was selected for Uljanik bulk carrier.

3.3. RANS optimisation

VICUS does not have its own in-house or commercial optimisation code for ESD design. Thus, a parametric model was be generated within the commercial code NX from SIEMENS and each geometry was exported in ^∗.igs format to STAR CCM+. STARCCM+ has the capability of working with the geometry model separated from the numerical model, so geometric modifications can be performed without modifying the numerical model, with the exception of re-meshing the model at each geometric change. This capability allowed VICUS to make any modification in a faster way, keeping constant the parameters of the numerical model and the post-processing reports and avoiding unnecessary numerical uncertainties. Moreover, each modification of the ESD geometry performed in CAD code does not imply having to import the whole geometry, but only the modified ESD geometry is imported to the base case computation.

Also, the lack of optimisation code for the design leads to perform a large number of numerical computations if it is wished to cover a substantial range of each variable involved in parametric study. This fact together with the possibility of having a reduced number of CPU resources would lead to a huge amount of time to perform the analysis if fine mesh is used. So, the medium mesh will be used in order to handle acceptable times for performing the parametric analysis. Later, the influence of this decision will be discussed.

Fig. 3.

Main geometric parameters for bulb design.

During the parametric study, some geometric constraints have to be respected, such as the propeller position and the aft perpendicular position. The main geometric parameters to define an optimised rudder bulb are listed below (see Fig. 3), being some of them referred to aft perpendicular position.

Bulb LE Diameter: diameter of the leading edge of the bulb (it has to be noticed the bulb is cut by a plane to allow to insert the hub-cap)

Bulb TE X-Position: location in x-direction of the trailing edge of bulb from aft perpendicular

Bulb Length: chord of the bulb

Bulb-Hub gap: distance in x-direction between the leading edge of bulb and trailing edge of hub-cap

Bulb max diameter: maximum thickness of the bulb

Bulb max diameter X-Position: maximum thickness of the bulb

Hub TE Diameter: location in x-direction of maximum thickness of the bulb

All the parameters were made non-dimensional using the diameter of the propeller, with the intention of comparing other rudder bulb designs from other ships.

The influence of each parameter was studied changing its value from three to five times, and a reference case was defined to determine the degree of influence of the parameter in the improvement.

Some constraints were imposed to some parameters, as it can be for the rudder bulb – hub cap gap. In theory, the gap between the hub cap and the forward part of the bulb should be as small as possible. In practice, there has to be a sufficient gap to allow the structural deflection under load and also tolerances that can be realistically achieved under real shipbuilding conditions.

The geometric variables used as an input are defined in the following section, the optimisation was carried out for one operational profile only.

More sophisticated techniques could have been used to maximize or to minimise the objectives functions, such as genetic algorithms or gradient-based algorithms. These techniques allow the determination of the best geometric configuration in a simple way, although it demands too much time and CPU resources for complex geometries and flows. As the code used was commercial (STARCCM+), and no parametric geometry can be defined in it, the implementation of theses genetic and gradient-based algorithms were not possible. Therefore, instead of using a methodology based on these kinds of algorithms (an automatic optimisation), a manual search between all the simulated configurations was performed.

3.4. Evaluation of ESD design

One of the most difficult tasks during the optimisation corresponds to the definition of the objectives functions. An objective function can be defined as an equation to be optimised given certain constraints and with variables which need to be minimised or maximised. These objective functions will be defined in terms of energy losses and in terms of propulsive and resistance values related to the propeller, hull and ESD.

Minimum total energy losses. Propeller losses due to hub vortex generation induce an under performance of the propeller-rudder. Vorticity field is the chosen parameter to quantify the energy losses downstream of the propeller and ESD. The vorticity is a vector field that describes the local spinning motion of a fluid in the space, in this case, at propeller wake field. It is calculated as the rotational of the velocity fields. It can be expressed by the formula: $\begin{matrix} \vec{ω} = \vec{\nabla} \times \vec{v} \end{matrix}$

Where $\vec{\nabla}$ is the nabla operator, × is the vector product (cross vector) and $\vec{v}$ is the vector field, being $v_{x}$ , $v_{y}$ and $v_{z}$ the velocity components in the director axis x, y and z, respectively. The vorticity will be plotted over a plane normal to the stream wise velocity so it can be expressed as scalar field multiplied by a constant unit vector $\vec{e_{z}}$ . $\begin{matrix} \vec{ω} = \vec{\nabla} \times \vec{v} = (\frac{\partial}{\partial x}, \frac{\partial}{\partial y}) \times (v_{x}, v_{y}) = (\frac{\partial v_{y}}{\partial x} - \frac{\partial v_{x}}{\partial y}) \vec{e_{z}} \end{matrix}$

With the aim of plots, the areas with highest vorticity are visualised, and therefore, how geometric modifications can be made to reduce those rotational energy losses.

In order to compare with more accuracy, the vorticity will be integrated over the plane to quantify how rotational flow is. Then the integral is computed over the surface S as $\begin{matrix} \overline{ω_{z}} = \int_{S} \vec{ω} d \vec{S} \end{matrix}$

This integral can be used as an objective function for the optimisation software to achieve an optimal and efficient ESD.

Larger vorticity of the fluid in the propeller wake is synonymous to the larger rotational propeller losses so it has to be diminished during the ESD design when two cases are compared.

Minimum resistance. Energy loss reduction occurs with drag reduction. The resistance is the resultant of the sum of surface forces, and it is obtained from $F = F_{p} + F_{s}$ , where both terms represent pressure and shear forces, respectively. They are defined as $\begin{matrix} \{\begin{matrix} F_{p} = \oint_{S (t)} p (s, t) d S \\ F_{s} = \oint_{S (t)} μ \frac{\partial u (s, t)}{\partial n} d S . \end{matrix} \end{matrix}$

Where p is the pressure and u the relative velocity of the surrounding fluid, $S (t)$ is the surface of the vessel and μ the dynamic viscosity. Numerical simulations without the propeller have had to be carried out to quantify the resistance using the previous definitions over the whole vessel and over the ESD geometry. A reduction of resistance leads to a reduction of propeller thrust, and in the most cases, a higher propulsive coefficient.

Maximum propeller thrust/torque coefficients ratio. The figure of merit given by the ratio between propeller thrust and torque gives an idea of how efficient is the propulsion unit since it shows how much delivered thrust can be achieved by delivered power unit. This figure of merit can be seen as a measurement of propeller efficiency.

The delivered thrust, T, is measured directly from the simulation, as a surface integral of pressure and shear forces over the surface propeller, while the torque, Q, is measured as a surface integral of cross product of distance by the total forces (shear and pressure forces). $\begin{matrix} \{\begin{matrix} Q = \int_{S} (\vec{r} \times \vec{F}) \vec{a} d S \\ T = \int_{S} \vec{F} \vec{n} d S . \end{matrix} \end{matrix}$

These forces and moments produced by the propeller are expressed in the form of non-dimensional terms: thrust coefficient, $K_{T}$ , and torque coefficient, $K_{Q}$ . The non-dimensional terms are expressed as:

Thrust coefficient

\begin{matrix} K_{T} = \frac{T}{ρ n^{2} D^{4}} . \end{matrix}

Torque coefficient

\begin{matrix} K_{Q} = \frac{Q}{ρ n^{2} D^{5}} . \end{matrix}

Where n is the propeller rotational speed, D is propeller diameter and ρ is the fluid density. The ratio of these two coefficients is the objective function to optimise, since it can be seen as propeller efficiency, as long as the loading condition does not change during phase design.

This figure of merit is used to compare simulations of the same parameter during the parametric study.

Maximum QPC. It has to be kept in mind that the ESD modifies the working point of the propeller so readjustment of rotational speed or propeller pitch has had to be done in order to balance the resistance force and propeller thrust.

The quasi-propulsive coefficient is the efficiency of the propeller working in the behind condition. Unlike the maximum propeller thrust/torque objective function, this takes into account the variation of loading conditions. It can be defined as a relationship between effective power and delivered power: $\begin{matrix} QPC = η_{D} = P_{e} / P_{D} . \end{matrix}$

Where $P_{e}$ is effective power and $P_{D}$ is delivered power, although it has also been derived from the product of these efficiencies: $\begin{matrix} QPC = η_{D} = η_{H} η_{R R} η_{o} . \end{matrix}$

Where $η_{H}$ is the hull efficiency, $η_{R R}$ is the relative-rotative efficiency and $η_{o}$ is the open-water efficiency.

The propulsive efficiency, $η_{D}$ , is expressed as the product of behind propeller efficiency, $η_{B}$ , which shows how the propeller is working when it is placed behind a vessel, and another coefficient $(1 - t)$ , related to the augmentation of pressure drop due to the presence of the propeller and the acceleration of the flow at the aft section of the vessel $\begin{matrix} η_{D} = \frac{V_{a} K_{T}}{2 π n D K_{Q}} (1 - t) = \frac{J K_{T}}{2 π K_{Q}} (1 - t) = η_{B} (1 - t) . \end{matrix}$

Where: $V_{a}$ is the vessel speed of advance, J is the advance ratio and t is the thrust deduction.

The first coefficient, $η_{B}$ , is easily calculated from values obtained by “self-propulsion simulation” whereas the last one $(1 - t)$ , have to be calculated from a towing or resistance simulation (numerical simulation without propeller). It has to bear in mind that behind simulations are performed instead of self-propulsion simulations since the thrust generated by the propeller does not balance the resistance of the vessel. A final self-propulsion simulation has to be performed to determine with accuracy the real improvement.

It is clear that the propulsive efficiency has to be improved to achieve an optimal ESD design.

Viewing the expression, a good ESD design is one that has high thrust and low torque and thrust deduction. High thrust and low torque can be achieved basically reducing rotational losses but this increment in the thrust usually leads to an increment of propeller suction and therefore, an increment of thrust deduction. So, a balance between these variables have to be done during design step.

3.5. Final selection

Finally, whether more than one ESD is designed (which is not the case here), a self-propulsion computation with both ESD is performed to determine a plausible improvement due to a positive interference, comparing the previous figures of merit. In case of negative interference, the best ESD is chosen.

This self-propulsion computation would be performed using frozen rotor approach and a fine mesh.

4. Bulk carrier design case

As stated previously, Uljanik shipyard proposed one of its bulk carrier as full scale validation vessel for the ESD design. Each partner, MARIN, HSVA and VICUS, have designed an ESD for this vessel using its own design methodology and tools. VICUS decided to design a downstream device, a Rudder Bulb. Then, a cross check has been carried out to determine which will be the ESD to manufacture. HSVA Pre-Swirl Stator has been selected and manufactured on the Uljanik bulk carrier. In this paper, the concept design of the rudder bulb is presented.

Fig. 4.

Picture of the bulk carrier “VALOVINE”.

4.1. The ship and design condition

“VALOVINE” (see Fig. 4) is the name of the selected Uljanik bulk carrier which main dimensions, engine data and propeller main characteristics are shown respectively in Tables 1–3. A speed of 15 knots has been selected for the design condition according to the operational profile of the Uljanik bulk carrier. The rotational speed of the propeller is 123 rpm. Table 4 presents the dynamic trim and sinkage for the design condition.

Table 1
Ship main dimension and coefficients of Uljanik Bulk Carrier

Ship Particulars Ballast Design

Length between Perpendiculars $L_{P P}$ 182.00 m 182.00 m

Overall Beam $B_{O A}$ 32.24 m 32.24 m

Draught at forward perpendicular $T_{F}$ 4.6 m 11.00 m

Draught at aft perpendicular $T_{A}$ 6.6 m 11.00 m

Draught at midship T 5.6 m 11.00 m

Displacement volume moulded ∇ 25673 $m^{3}$ 54530 $m^{3}$

Wetted surface $S_{S}$ 6292.3 $m^{2}$ 8656.4 $m^{2}$

Block Coefficient $C_{B}$ 0.7173 – 0.8235 –

Ship Particulars	Ballast	Design
Length between Perpendiculars	$L_{P P}$	182.00	m	182.00	m
Overall Beam	$B_{O A}$	32.24	m	32.24	m
Draught at forward perpendicular	$T_{F}$	4.6	m	11.00	m
Draught at aft perpendicular	$T_{A}$	6.6	m	11.00	m
Draught at midship	T	5.6	m	11.00	m
Displacement volume moulded	∇	25673	$m^{3}$	54530	$m^{3}$
Wetted surface	$S_{S}$	6292.3	$m^{2}$	8656.4	$m^{2}$
Block Coefficient	$C_{B}$	0.7173	–	0.8235	–

Table 2

The engine data of the Uljanik Bulk Carrier

	Engine data

Sign	Term	Value	Unit
$P_{B}$	Engine break power (100% MCR)	8600	kW
N	Rate of revolution	121	Min^–1

Table 3

The propeller Particulars and Characteristics

Propeller Particulars and Characteristics		Full Scale
Propeller Diameter	$D_{P}$	5.800	m
Hub Diameter	$D_{HUB}$	0.858	m
Number of Blades	Z	4
Rotation	–	Right Handed
Nominal pitch Ratio	$P / D_{0.7 R}$	0.715
Expanded area ratio	EAR	0.587

Table 4

Dynamic trim and sinkage for design condition

Dynamic Trim and Sinkage Loaded [15kts]
Trim (positive nose down)	0.178	deg
Sinkage (positive downward)	0.276	m

4.2. Concept design of the Rudder Bulb

Numerical settings. The mathematical model used for the calculation of the numerical simulations is described by Reynolds Averaged Navier Stokes Equations (RANSE). The Reynolds stress tensor was modelled to close the governing equations by means of a two-equation model, named Two Layer K-Epsilon, with a Two Layers All $y +$ Wall Treatment for the wall modelling. The problem is closed establishing the initial and boundary conditions on the physical and computational boundaries.

The physical domain is discretized by means of unstructured mesh of polyhedral cells. Several refinement zones or volume shapes were located at different parts of the domain, particularly in the wake region, in order to increase the density of cells and improve to the resolution of flow features. The whole mesh consists of a total of about 1.5 millions of cells, where the rotating region (propeller) has about 200.000 cells and the fixed region 1.200.000 cells.

For all cases, the $y +$ values were in a range between $y + = 30$ and $y + = 150$ with an average of 50.

RANS Evaluation. Due to short period of time to design the ESD, the number of computations was reduced, so the influence of thrust deduction on propulsive efficiency was calculated according to the following argumentation. Since the thrust deduction is related to the hull resistance augmentation due to the propeller working in behind condition, the influence of last coefficient on propulsive efficiency is calculated using the hull resistance $(R_{B})$ value got from behind simulation. The variation of resistance gives an idea on how the thrust deduction changes due to the presence of the ESD.

So the different ESD designs were compared against the original one by new figure of merit, named net gain. The net gain is calculated as the sum of the improvement of the propulsive efficiency ( $η_{P}$ ) and the reduction of the hull resistance in behind condition ( $R_{P}$ ) and it is expressed as: $\begin{matrix} % Net gain = η_{P} - R_{P} . \end{matrix}$

Where each one of these coefficients are defined as $\begin{array}{rcl} η_{P} & = & \frac{η_{B - ESD}}{η_{B}} - 1 \\ R_{P} & = & \frac{R_{B - ESD}}{R_{B}} - 1 . \end{array}$

Where $η_{B - ESD}$ and $η_{B}$ are the propeller behind efficiency with and without ESD, respectively and $R_{B - ESD}$ and $R_{B}$ , (as before) are the hull resistance in behind condition with and without ESD, respectively.

Indeed, with the aim of performing a higher number of computations for the short period of time, a medium mesh was used for all computations during the design step.

Instead of performing a parametric analysis, several bulbs with different thickness, length, sharp fore bulb, different curvatures fore bulb, etc. were analysed (see Fig. 5). The improvements achieved for all computations were not so high, always lower than 1%. The best one was the case 5, which was shared with the partners.

Fig. 5.

Example of simulated bulb geometries.

After sharing the bulb geometry with the partners, a computation with finer mesh was performed (for cross check validation) leading to a new result: a deterioration of propulsive efficiency in respect to bare hull. Therefore, the medium mesh was not enough to retain all physical phenomena around propeller, rudder and ESD, so a description of the design process is not presented here, because not useful.

Finally, it has to be mentioned that these numerical simulations were computed at model scale.

Other effects of Bulb. The lateral force does not indicate how efficient the ESD is but it gives an indication on how its presence affects to the course-keeping of the vessel, i.e., how the behaviour of the vessel is when it sails in free run. As it was commented before, there is a force unbalance due to the asymmetry of the propulsion system which modifies the flow differently on port and starboard sides depending on how the propeller rotation is for single screw vessels. This asymmetry of the flow leads to a different pressure gradient on both sides of the ESD and as consequence a side force appears. In this case, due to the presence of right-hand side-screw along with the wake of the ship, a positive side force of the propeller is produced. The swirl and acceleration induced by the propeller alter the speed and incidence of the flow feeding into the ESD, leading to a positive side force. Therefore, the presence of bulb deteriorates the course-keeping of the vessel, although in a little way since the increase of side force is small (about 5% higher).

4.3. ESD cross check and selection

Three ESDs have been designed for the full scale validation vessel: a Pre-Swirl Stator by HSVA, a Pre-Duct by MARIN and a Rudder Bulb by VICUS. In the previous sections, the design methodology of the Rudder Bulb has been presented. In order to select the ESD that would be manufactured, a cross check of the three ESDs has been carried out by all three partners. This section presents the results of the cross check obtained by VICUS. The cross check of the other partners is not shown here even if the tendency of the results is the same. The results obtained for the different ESDs are comparable since the same numerical models and meshes have been used to perform the simulations by VICUS.

The same numerical model was employed for the analysis of each ESD. The total number of cells for meshes containing HSVA PSS, MARIN Duct and VICUS bulb are around 8 million. Slight difference in the number of cells can be found for all of them due to the ESD geometric features.

The numerical simulations were carried out keeping constant propeller rpm and vessel speed. The results are presented in Table 5. Both MARIN and HSVA pre-swirl ESDs lead to an important increase of thrust since they modify the incoming propeller wake. The ESDs increase the velocities, basically, on the upper portside part of the wake reducing the Taylor wake, moving the working point in open water test to lower advance ratio. The difference between both upstream devices is minimal. The post-swirl, VICUSdt ESD, barely increases the propeller thrust since the ESD shape is not able to modify the propeller wake.

Table 5
Results for cross-check verification by VICUS

$K_{t}$ $K_{q}$ $K_{t}$ / $K_{q}$ $η_{B}$ Gain Rp Net Gain

ESD [–] [–] [–] [–] [–] [–]

None 0.162 0.022 7.5 0.776

MARIN 0.193 0.025 7.8 0.808 4.1% 1.9% 2.3%

HSVA 0.195 0.025 7.8 0.807 4.0% 0.3% 3.7%

VICUSdt 0.168 0.023 7.4 0.766 −1.4% 0.9% −2.2%

	$K_{t}$	$K_{q}$	$K_{t}$ / $K_{q}$	$η_{B}$	Gain	Rp	Net Gain
ESD	[–]	[–]		[–]	[–]	[–]	[–]
None	0.162	0.022	7.5	0.776
MARIN	0.193	0.025	7.8	0.808	4.1%	1.9%	2.3%
HSVA	0.195	0.025	7.8	0.807	4.0%	0.3%	3.7%
VICUSdt	0.168	0.023	7.4	0.766	−1.4%	0.9%	−2.2%

Torque coefficients are higher for all ESD designs in respect to the case without ESD. The higher reduction on advance ratio, the higher increment on torque coefficient is achieved. Both upstream ESDs have the same increment in thrust coefficient whereas the difference is negligible for downstream device.

The propulsion performance shows MARIN ESD as the best ESD although HSVA ESD has little lower value. The improvements are around 4%. The value of propulsion performance of VICUSdt ESD needs a special mention. During the design phase, a too coarse mesh was used implying a wrong estimation of the improvement.

To determine the total gain of the ESD, the effect of the propeller performance on hull has to be calculated. The resistance of MARIN ESD is increasing of around 1.8% whereas HSVA ESD only goes up of 0.3%. Since the propeller performance is the same for both ESDs, the loss resistance should be the same but it is not. So, the difference on resistance must be due to the influence of the ESD on the hull.

It has to be mentioned that all figures from previous table do not correspond to a real self-propulsion point since the simulations were carried out at the same operational profile defined for the vessel without ESD, and the presence of ESD increases the net thrust and torque. Then, these simulations should be simulated in an operational condition with lower rpm than original one to work at the adequate point.

5. Conclusions

The hydrodynamic methodology to design an ESD (Energy Savings Device) developed in the FP7 EU project GRIP by VICUS has been explained. This methodology was applied to design a Rudder Bulb into a new build 52,000 DWT Bulk carrier by Uljanik shipyard in Croatia without too much success.

The methodology is based on double-body RANS computations on two different meshes, medium and fine mesh, without any optimization code. The fine mesh is used to perform a computation of bare hull to evaluate the potential viability to save energy using an ESD and to determine the achieved savings due to the installation of designed ESD. The medium mesh is used to analyse the sensitivity of each geometric parameter that defines the ESD. The sensitive analysis determines the best operation range of each geometric parameter to improve the efficiency and, the best points of each range are selected to design the new ESD.

The performance of each ESD configuration is analysed by integral values of resistance and propulsive coefficients and by flow analysis. On the one hand, the integral values give the best criteria to select one configuration respect to another one, since it is a direct comparison. Also they give the net improvement with respect to bare hull. On the other hand, the flow analysis allows to know why the ESD design works or not, giving the needed information to get an optimized ESD.

In GRIP project, an ESD was designed by each partner employing its own methodology, and the best one would be installed on Uljanik Bulk Carrier. The tight schedule along with available hardware and software resources do not allow to apply the hydrodynamic design methodology. So a modified methodology was applied to design a rudder bulb but without any success from the point of view of improvement. In addition of cited VICUS Rudder bulb, a Pre-Swirl Stator (PSS) and Pre-Duct were designed by HSVA and MARIN, respectively. The results from cross check verification show that the best one corresponds to PSS by HSVA, which was designed using an in-house RANS-QCM coupling method. Therefore, VICUS procedure, at least, was able to determine the best ESD.

The bulb has to be able of harnessing the rotational energy losses that travel downstream from the propeller hub cap, in order to improve the propulsive efficiency. These rotational energy losses are associated to low pressure core (hub vortex) that appears on propeller hub cap due to the rotation of the propeller. Successful ESD design can be achieved if it can reduce these energy losses.

The described methodology demands too much time and CPU resources since it forces to perform a lot of RANS computations. So if the schedules for designing ESD are tight on time, the methodology should be changed. It would be recommended to use some numerical methods which demands low time and resources, such as vortex lattice method or potential method, among others. Therefore, more research has to be done.

Footnotes

Acknowledgements

The research leading to this work has received funding from the European Union Seventh Framework Programme (FP72007-2013) under grant agreement n°284905: Green Retrofitting through Improved Propulsion.

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Xing-Kaeding, Bulk carrier pre swirl stator validation, 2015, ISP.

User Guide. Star-CCM+ V8.04.

Xing-Kaeding, ESD design for a validation bulk carrier, 2015, ISP.