Mitsubishi Heavy Industries Technical Review Vol. 50 No. 2 (June 2013)
50Application of Advanced CFD Technology
to Energy-Saving Hull form Development

MAKOTO NISHIGAKI*1 MAKOTO KAWABUCHI*2SATORU ISHIKAWA*3

Due to the advancement of computational fluid dynamics (CFD) technology, CFD can copewith many cases of hull form development. Mitsubishi Heavy Industries, Ltd. (MHI) evaluates hull
resistance and propulsive efficiency using the most of the latest CFD technology, which can berobustly applied to wave-making computation in consideration of free surface against complex
forms of hulls and appendages, as well as propeller-considered self-propulsion computation at ahigh degree of accuracy and speed, while deriving refinements for forms of hulls and appendages
from information such as the circumstances of waves created by the hull and flow around the hull.
We will continue to use such technologies to further improve the energy-saving performance ofvessels.

|1. Introduction
While CFD technology is making remarkable progress, in a bid to be effectively applied todeveloping energy-saving hull forms, it is an important factor, as well as to have an estimatedaccuracy sufficient to derive refinements, to be able to quickly generate grids so that performancecan be evaluated for complex forms of actual ships, to be able to robustly correspond to analyses
including free surface and to be able to perform large-scale grid and numerous computations at ahigh speed. Using the latest CFD software and large-scale parallel computers that meet these goals,
MHI is performing wave-making and self-propulsion computations to promote energy-saving hull
form development, which is introduced in this report with examples.

|2. Computing method
2.1Wave-making computation

Optimization in the shape of stern edge is essential for the development of energy-saving hullforms, as it seriously affects the properties of stern wave-making and consequently the ship’s
propulsive performance. With the existing CFD method for free surface flow using structured grids
and the surface tracking method, in which grids are transformed in accordance with changes in thewater surface, CFD was not fully used to actually design the stern edge form, since the expert
knowledge/time required for grid generation as well as the robustness of the computation was
limited As a result, MHI has been shifting to unstructured grids and the surface capturing method,in which grids are fixed and free surface analysis uses a density function, with the aim ofestablishing a more robust computing method. As unstructured hexahedral grid technology
advanced, it is now likely that high-quality grids can be generated in a short time, even for complex
geometries. As for the surface capturing method, it is also likely that robust wave patterns can beacquired at a high degree of accuracy as multi-purpose CFD code technology advanced.
Previously, the number of grids has been limited due to computing capability, resulting in*1

Chief Staff Manager, Nagasaki Research & Development Center, Technology & Innovation Headquarters*2

Nagasaki Research & Development Center, Technology & Innovation Headquarters*3

Senior Manager, Nagasaki Research & Development Center, Technology & Innovation Headquarters

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rough grids in areas distant from the hull and dense grids only in areas close to the hull, and wehave been striving to reduce wave-making resistance caused by the divergence wave (八-shapedwave) splitting from the bow, setting the wave profiles as a major evaluation index. However, toperform more accurate computing, it is desirable to expand the range of grid fragmentation, andwhen reviewing the stern form in particular, we expanded the range of grid fragmentation aroundthe free surface in the rear part of the hull as well, as the state of transverse waves there will also
matter. Because the automatic mesh generator is used to generate unstructured grid, factors such as
the number of grids in the corresponding parts are not fully fixed between the two hull forms being
compared, unlike in the structured grid. To prevent grids from affecting computing results, thenumber of grid compartments has to be increased more than in the structured grid.
Considering these factors, the number of grids was increased from the previous hundreds ofthousands level to the million to tens of millions level. Table 1 shows a comparison of the existing
CFD and the latest CFD computing methods, while Figure 1 shows an example of computed gridcomparisons around the stern and Figure 2 shows a comparison of computing results. It can beseen that the latest CFD can capture a broad range of wave-making circumstances, while truly
reflecting the stern form and sharply increasing the number of grids.
Table 1Comparison of previous CFD and latest CFD methods

Hundreds of thousands

Latest CFD
Complex geometry truly
accounted for
Unstructured hexahedral grid
Surface capturing method 2) (VOF3))
Millions to tens of millions

Body force model by UQCM 4)

Body force model by UQCM 4)

Turbulence modelSR222 revised Baldwin Lomaxmodel (0 equation)

SST k-ω (2 equation)

Number of CPUs used in parallel
computing

1

16-64

Treatment of stern shape
Grid type
Treatment of free surface inwave-making computation
Grid numberPropeller model in self-propulsion
computing

Previous CFD
Modified or simplified to ensurestable computing
Structured grid
Surface tracking method 1)

1) Method that transforms grids in accordance with changes in free surface
2) Surface capturing method: A method to analyze free surface by density functions using fixed grids
3) VOF: Volume of Fluid
4) UQCM: Unsteady Quasi-Continuous Method

Figure 1 Comparison of wave-making
computation grid using previous
CFD (left) and latest CFD (right)(RoRo vessel)

While the transom was extended and the stern
tube was curled to ensure computing stability
with the previous CFD using a structured grid,stern geometry is truly reflected and the numberof grids is greatly increased with the latest CFD
using unstructured hexahedral grids.

Figure 2 Comparison of wave-making
computation results by previous
CFD (left) and latest CFD (right)(KRISO container ship)
The latest CFD captures the wave extending
obliquely backward from the bow and the stern
in a wide range.

Figure 3 shows an example of comparisons between an experiment and the wave patterncomputing results using the latest CFD, in which the positions and heights of longitudinal andtransverse waves were mostly in agreement between the experiment and CFD.

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Figure 3 Comparison of wave patternexperiment and CFD (ferry)
Red and blue represent high and low wave heights,
respectively, in this contour map. Position andheight of divergence waves and transverse waves
are largely in agreement between experiment andCFD.

Figure 4 shows a comparison of local wave-making circumstances near the stern with aphoto. The form of wave-making captured by CFD agrees with the experiment result on the sideedges at the end of the stern.

Figure 4 Comparison with experimentphoto of wave-making around stern(ferry)This shows a comparison of CFD (bottom left) andmodel experiment (top: photo, bottom right:
measuring result) of the local wave circumstances
behind the stern of a ferry.
The form of waves extending obliquely backwardfrom both corners of the stern agrees in CFD andexperiment (red dot-lines in figures below), whichlooks white in the experiment photo.

2.2

Self-propulsion computing

MHI has evaluated the effect of propeller inlet flow by incorporating the UQCM (UnsteadyQuasi-Continuous Method) propeller computing method as a body force propeller model. We
performed self-propulsion computing by incorporating the same method with the multi-purpose
CFD code.
In addition, we performed this self-propulsion computing without taking free surface intoconsideration (in symmetrical condition) due to issues concerning the stability and computing time.
So, computed grids are different from those created by wave-making computation. Like
wave-making computation, however, we used an unstructured hexahedral grid and truly reflected
the complex geometries in front of and behind the propeller. As developed boundary-layer flow
enters the spaces in front of and behind the propeller, we tried to increase the accuracy byincreasing the grid density higher than usual in these areas. The number of grids reached themillions, one order larger than in other areas, by parallel computing using multi-purpose codes.
Figure 5 shows the estimate accuracy of self-propulsion factors (t: thrust deduction
coefficient and wm: wake fraction) computed by the aforementioned self-propulsion computing
method. Challenges remain in the estimate accuracy, with the wm computed by CFD generallyindicating lower figures than those acquired from basin experiments, for example. Accordingly, weare currently estimating self-propulsion performance by always comparing CFD results withexperimental results. We will continue to improve the method and leverage the results for
improving a stern form that boasts superior self-propulsion performance.

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Figure 5

Estimate accuracy of self-propulsion computing using body force propeller model

The thrust deduction coefficient (t) and wake fraction (wm), which are self-propulsive factors, exhibit good
mutuality between the experiment and CFD. Given a few challenges including the smaller wm evaluation
than in the experiment, estimation is always carried out in comparison with experimental results.

|3. Computing examples
To develop energy-saving hull forms using the computing method mentioned above, analysisof the flow around the hull is very important. In this section, we will explain the accuracy of flow
evaluation using three examples, namely the review of improvement in the stern edge shape using
the stern wave height evaluation, flow field evaluation for twin-skeg hull forms and flow field
evaluation of the propeller plane behind the shaft bracket, all of which have been difficult using
existing CFD computing.

3.1

Evaluation of stern wave patternFigure 6 is a contour map of a wave pattern by CFD computing for the hull of a high-speed
ship before and after improving the stern edge shape. As a result of hull form improvement, waves
were lowered immediately behind the stern edge and posterior. Figure 7 shows a comparison ofresidual resistance in the experiment and CFD computation on these two hull forms, which exhibit
the accuracy of CFD computing showing that the hull form improvement resulted in lower residualresistance.

Figure 6 CFD comparison of stern
wave heights before and afterimprovement in stern edge shape(ferry)This shows that the wave heights behind thestern are lowered as a result of theimprovement in the stern edge shape.

Figure 7
Resistance reduced bydifferent stern edge shapes (ferry)This shows CFD also captures resistance
reduced in a broad range by improvements inthe shape of the stern edge.

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3.2

Evaluation of flow field of twin-skeg hull form

When developing a twin-skeg hull form as shown in Figure 8, evaluating the asymmetricnature of the flow field inside and outside of the skegs becomes important. Shown in the same
Figure 8 is a comparison of flow lines between the skegs acquired by paint testing and CFD
computing, and the position and forms of the flow separation line, which can be observed in bothresults, are similar to each other.

In the paint test, in which whitepaint coated on the model ship
extends like numerous threads inthe direction of the flow, the paint
did not extend between the skegs
above the red dot-lines in thefigure, indicating flow is breaking
away in this area.
CFD also shows a state where flow
focuses on this area and forms a
separation line (however, flow lines
can be still seen above theseparation line as CFD indicatesflow lines even when they areslow).

Figure 8Twin-skeg Hull Form and Flow between Skegs

Figure 9 shows a comparison of the flow field on the propeller plane on the port side. Astrong upflow can be confirmed between the skegs, while inward flow from outer side is generated
down below, making the wake at the bottom edge of the skegs flow inward. CFD also captured
these characteristic flow trends. In this manner, CFD computing can efficiently evaluate flow field
circumstances in detail, even when it is such a complex stern form such as a twin-skeg, and lead tofurther hull form improvement using this flow field information as a reference.

Figure 9

Flow field on propeller plane of twin-skeg hull (left propeller)

The bluer the contour map is, the faster the relative flow rate is against the hull. The upflow
strengthens between the skegs. Inward flow from outer side down below is making the slow
zone behind the skeg flow inward. CFD captures these circumstances as well.

3.3

Evaluation of flow field on propeller plane behind shaft brackets

Figure 10 shows the pressure pattern of a hull form embedded with shaft brackets and thepropeller plane flow field behind the shaft brackets. In the flow field on the propeller plane, a totalof three wakes including that of shaft itself between the wakes of the two brackets can be seen, andthis property of the flow field is captured by CFD computing.

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Figure 10 Shaft bracket-embedded hull form’s pressure pattern and flow field
on propeller plane (left propeller)
A total of three relatively slow zones are generated in the lower course of the shaft itself andtwo brackets by upward and inward flow seen in the flow field vectors on the propeller planes,
which is also captured by CFD.

|4. Conclusion
MHI established a practical CFD method that can evaluate the effect of a complex hull form
near the stern or appendages on a ship’s performance and flow fields, which are significant factors
when developing an energy-saving vessel, by using the latest CFD technology capable of large
scale unstructured grids (hexahedral grids) on a scale of millions to tens of millions, as well as
robust free surface analyses and high-speed computing based on parallel computers. We are
improving the energy-saving performance by applying this method to evaluating wave patterns, theflow field of the twin-skeg hull form and the propeller plane flow field behind the shaft bracket,etc,, which have been difficult to evaluate, in order to derive refinements from the flow field
information. From now on, MHI will continue to establish a design method considering scale effectand ship resistance waves, focusing on ship performance in actual seas.

Reference
1. Takada et al., Journal of The Japan Institute of Marine Engineering No. 197 (2002) p.63