The algorithm described in the preceding sections was used to optimize the hull and propeller of a KCS SIMMAN container ship. The original hullform can be seen in Figure4.14. Through the optimization the length, 230 meters, and the displacement, 49620.6 cubic meters, was kept constant. The vessel is also assumed to have two L51/60DF engines MAN (2009) on board, each with a 5-bladed B-series propeller.
Figure 4.14: Original container ship hullform.
The optimum design vector was x∗ =
3.065 0.9 1.066798 0.878813 8.0
. This shows that, in the optimal design, the propeller diameter went to its maximum allowable dimension, while the beam went to its minimum. This is expected given the simplistic representation of the hull used in this work. The optimum design vector leads to a lifetime fuel consumption, LF C∗, of 1.19 million barrels for the ship.
In order to investigate the potential of the simultaneous method proposed in this work it must be compared to a similar exercise using a point-based sequential approach. This is done by formulating two separate optimization problems; one for the hull and one for the propeller, at a given design speed. The optimization problem for the hull is found in equation 4.25.
minimize RT(x, V0)
with respect to 1.2≤ B/T ≤ 3.6 5.0 ≤ L/B ≤ 8.0 subject to 0.4≤ Cb ≤ 0.8
8.8 ≤ T ≤ 12 (4.25)
a speed of 12.35 meters per second was used. Running this algorithm will produce an optimum beam to draft and length to beam ratio corresponding to a minimum resis- tance, R0
T. This resistance is then used to solve the propeller optimization problem
seen below in equation 4.26.
minimize − N(x, V0, R0T) with respect to 0.5≤ D/T ≤ 0.9
0.5≤ P/D ≤ 1.4 0.55≤ Ae/Ao ≤ 1.05
subject to τc− τc,max ≤ 0 (4.26)
In equation 4.26 N is the efficiency corresponding with the design vector x, at the speed V∗ and resistance R∗
T. Solving the optimization problems given in 4.25
and 4.26 sequentially will produce a design vector which can be used to calculate a corresponding LFC value. When this process is executed on the KCS SIMMAN con- tainer ship, a solution, x0 =
2.662 0.9 1.115079 0.882906 8.0
is found. This leads to a fuel consumption of 1.337 million barrels. A comparison of the two results can be seen in Table 4.3.
Table 4.3: Comparison of results for different optimization methods.
Method B/T D/T P/D Ae/Ao L/B Cb T (m) LF C (bbl× 106)
Simultaneous 3.065 0.9 1.07 0.879 8.0 0.8 9.38 1.199 Sequential 2.662 0.9 1.12 0.883 8.0 0.7 10.8 1.337
Table 4.3 shows that there is a 10.36% fuel savings realized when using the si- multaneous optimization over the sequential approach. The differences in the two design vectors come from both the simultaneous optimization and the probabilistic approach. The B/T value of 3.065 for the optimal vessel is the result of optimizing over the entire operational profile, instead of a single design speed. The differences in
the variables describing the propeller, P/D and Ae/Ao, are largely the result of the
simultaneous optimization. This shows that by considering the propeller and hull as a coupled system, even in the simplified representation shown in this work, consider- able fuel savings can be found over the life of a vessel. The two methods also found fairly different hullforms in terms of shape, with the simultaneous method favoring a higher block coefficient and lower draft and the sequential method finding the oppo- site. This shows that by utilizing multi-disciplinary design techniques it is possible to explore the naval design space and reveal aspects of it that may be difficult to otherwise ascertain. Given the difficulty of the naval lifetime cost problem, the work presented in this section highlights the potential to use multi-disciplinary techniques to facilitate the development of three dimensional trade-spaces comparing different categories of lifetime cost.
4.3
Contributions
The work shown in section 4.1 has developed and demonstrated the ability of a novel early-stage design method to develop trade-spaces for build complexity and resistance. This method has been demonstrated by producing these Pareto fronts for two different hullforms; a nominal naval combatant and a container ship. These two hulls differed significantly in both shape and mission and the optimization formulation presented was able to capture these differences and search a large portion of the design space around the original vessels. By utilizing a search method such as this the focus of the optimization becomes informing the designer to the nature of the design space, allowing them to make decisions that support the reduction of lifecycle costs.
While the optimization exercise shown here represent a small portion of the crite- rion necessary to analyze during ship design, they highlight the potential benefit to understanding this type of trade-space during the time when design decisions can still
be made. It has also been shown that the nature of these trade spaces, while possibly having similar trends, can have varying shapes and may not be entirely intuitive from the outset. The aspects of the design that are changed along this trade-space are also not necessarily evident and this methodology allows these aspects to be explored and better understood. Thus, a tool such as the method presented here could give a designer the ability to make changes to a hull form early in the design process and know how they will impact different life-cycle cost aspects.
It has been shown that, especially for the naval combatant, the trade-space can be difficult to resolve; and the work presented here produced an incomplete Pareto-front. It is believed that this is due to the unique nature of a warship’s mission requirement. The shape coupled with the complex operational profile creates a design space that is difficult to explore and, yet, important to understand. This shows that there is a potential to employ more powerful optimization techniques; such as multi-disciplinary optimization methods, to create a framework that is able to resolve Pareto-fronts between competing categories of cost for complex mission types.
Thus, in section 4.2 it has been shown that multi-disciplinary optimization rou- tines can be used effectively in the naval design space. The work presented a new approach to minimize the lifetime fuel consumption of a vessel by simultaneously opti- mizing the hull and propeller geometry for a vessel. The approach uses a probabilistic mission profile to describe the operation of the vessel in order to avoid optimizing for a single speed. This simultaneous method has shown noticeable improvements in fuel consumption over a traditional sequential point-based approach and converged to dif- ferent hull and propeller geometries. An algorithm such as the one shown here could aid in the early stage design process, allowing systems to be developed which min- imize the lifetime fuel consumption and, therefore, reduced overall ownership costs and emissions.
clear that the lifetime cost space is a difficult one to explore. In chapter 3 the maintenance-production design space, even for a simplified problem, contained a knee in a near-90 degree Pareto-front. In this chapter the Pareto-front found when com- paring producibility and resistance was difficult to resolve for the naval vessel. Thus, it is necessary to develop a way to more effectively resolve these fronts to understand the trade-offs between different categories of cost. In the next chapter a method to do this will be presented, utilizing the concepts of multi-disciplinary optimization and specific enhancements to facilitate solving this problem.