Automatic CFD Optimizing of Hull Forms Using Strategy-Driven Transformation Functions

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1 Automatic CFD Optimizing of Hull Forms Using Strategy-Driven Transformation Functions Clemens Koechert, TUHH, Hamburg/Germany, Abstract In contrast of generating hull forms more or less from scratch, the present method uses existing hull forms. This approach allows to improve manually optimised hull forms as they are available on ship yards. To reduce the search domain of possible changes to a starting hull, a set of transformation functions is used. These functions allow a systematic variation of hull characteristics. Generated hull forms are evaluated by CFD tools like the wave-resistance code KELVIN. Spline approximations in the optimization search space allow to reduce the number of actual CFD evaluations, accelerating the optimization process. The modular procedure allows exchanging individually optimization algorithm, different CFD solver, or target function. 1 Introduction Setting up a new vessel is a complex work flow. Most time is consumed for designing and optimising the ship s hull form to get best performance. As this progress is quite at the start of the design process, this must be very quick and as exact as possible. Designing ships by starting from scratch is a long, time spending procedure that is necessary if complete new types of vessels are developed. Due to the fact that a lot of reference vessels are normally available on a shipyard, new vessels typically will be based on existing vessels. For that case, it is not required to start from the scratch creating complete new lines, but it will be quite more efficient to further develop existing hull forms to solve the given problem. 1.1 Using a computer aided optimisation tool for hull forms Because every ship is a tailor-made object, there is a need for individual optimisation of hull forms. In the design process, some data like main dimensions or the size of cargo holds are given and cannot be changed easily. But mostly there will be enough design topics being customised for every special problem. In the early design process, a lot of parameters can be changed, so that it takes most time to find a good solution or even the best. To increase the speed of this design process, it is useful to perform a systematic variation of some global parameters concerning the vessel s performance. Nowadays this optimisation process is done manually, but this represents a time-consuming, monotonous work flow to the developer. Consquently, the developer is satisfied if the solution is quite better than the vessel of comparison, mostly limited by the given timetable in the design process. At the moment, only 10% of the given time is used for thinking about what kind of variation has to be done because 90% of the time is needed to modify the lines concerning the problem given before. This shows that now this design process is not effective and it would be quite more useful if the developer spended 90% of the time thinking about useful modifications and only 10% of the time for optimising the lines plan. This could be realized by using computer aid for hull-optimisation. So the basic idea with respect to this problem is that human s decide how the problem has to be solved instead of saying what has to be done to solve the problem. Implementing this idea leads to the main problems of the desired method: it has to be faster than human work. Unlike human beings, computers have no intellectual power to make predictions for desired transformations. This results in the fact, that for optimising hull forms more variations have to be calculated, particularly at the beginning of the optimisation process. The main focus while developing an optimisation algorithm has to be on the efficiency. In this context efficiency means that the algorithm needs not even to be the fastest in finding calculation points, it has to be efficient in case of using as few 523

2 calculation points as possible because the calculation time of every point is significantly higher then the optimisation time itself. For example, to perform an optimisation in every days work, the optimisation process should not take more than half an hour, so that in the moment 15 iterations can be calculated. For a long calculation taking time over a night, some more iterations are possible. The main intention of this project is that the developer s focus while designing vessels is shifted from making variations of hull forms, to thinking about what kind of variations are necessary to reach an optimal design. 2 Strategy-driven transformation functions During early design, the developer performs handmade hull form optimisation, After modifying the hull form, CFD-calculations have to be performed to check if the chosen strategy fullfills the prediction. For numerical representation of the hull designer s daily work, strategy-driven transformation functions can be suggested. The interaction between most methods used in the early design process can be automated without any problems. Setting up free variables describing the different transformation strategies do not result in a too big search area if variables are set to be independent to each other. This can be easily done, due to the fact that in normal work the design topics are treated sequentially, e.g. first optimising bulbous bow and after that finding the best bilge radius or lines. In the early design stage, absolute values e.g. resistance given by the modified hull form are quite not of interest. The main focus is on the trend of results in working with free variables because only after the last step absolute values are necessary to make a resistance prediction. Manually it is no problem to find good values, but for finding the optimum, mostly not enough time is given in the short early design phase. For automatic optimisation, policy-functions are more useful than fixed parameters. The main idea in using strategy-driven transformation functions is, that the hull form itselfes gives all necessary values to the optimising tool, the designer only decides what kind of transformation has to be performed. Because of just defining the chosen transformation function, the designer only has to set up the upper and lower boundaries of the free variable of the function. The functions used are free in definition, so that for every problem individual strategies can be defined. Due to the fact that an optimisation tool has to work with these functions, they have to be controllable by the selected optimisation tool. The value given back to the optimisation tool can also be a combination of results given by different tools, e.g. a transformation of hull form without following CFD-calculation is mostly not useful. The program ARGO is used for hull form transformations. Originally implemented in the early 80 s, the algorithms allow hull form transformations in very short time. Starting from an existing mesh, ARGO uses transformation functions depending on the local coordinate system to develop the new hull form. The transformations can be additive, the new value results in the old value adding the result of the transformation function in this point, or multiplicative where the new value is given by the old value multiplicated with the transformations functions result of the point. Having the definition that frames are always a plane with the x-axis as normal vector, the functions f 2 and f 3 are always set to one. x y z = x+ f 1(x) = y+ f 4(x) f 5(y) f 6(z) = z+ f 7(x) f 8(y) f 9(z) Such kind of hull form transformation are given in Fig.1. On the left side, a change of the bilge radius is done and the difference is shown in the plot of the two hull grids. On the right side, a transformation of transom immersion is shown and the different behaviour can well be seen. 524

3 Fig.1: Examples for hull form transformation, left: change in bilge radius, right: change of transom immersion Not every transformation leads to a fairing hull form, particularly if the input data results in transformation functions which can not be handled by the program. Because of that, transformation steps may have to be splitted into smaller ones and performed in sequence. 3 Optimisation Process In the optimisation process theoretically a global minimum can be found, but this would be very time consuming. A lot of calculations have to be done and manually it is quite impossible. Due to the fact that many values to be found are some kind of integers, like main engine scaled in available cylinders and vessel s breadth scaled in container breadths, the result only has to be better than a given limit. In consideration of performing calculations in an acceptable time limit, it is more effective to reduce the number of used calculation points than to get the best possible solution. The use of independent free variables leads to the possibility of separating the policy-functions into suboptimisation processes and solve them seperately. Only the results of these local optimisations will be used for the following global optimisation step (Fig.2).... Optimizer Optimizer Optimizer Method Method Fig.2: Optimising process depending on independent policy-functions 3.1 Optimising with independent variables using convex functions Searching the whole area to find the optimum is almost impossible because setting up a global mesh of calculation points is not practical. n calculation points = k n variables Setting the free variables independent to each other reduces the needed calculation points to n calculation points = (k 1) n variables

4 for each iteration. Using convex optimisation methods, only three knots are needed to set up a convex spline for each variable. This indicates a compact and fast system for optimisations: n calculation points = 2 n variables + 1 The optimisation tool now runs on an interpolated spline considering an increase of the local error between the interpolated spline and the calculated value in the target point. According to the fact that the results given by the free variables are not really independent, a new calculation or iteration step has to be done, starting in the found point or, if an optimum was found, a calculation has to be done to verify the values given by the optimiser. The calculation of the knot s values can be done parallell on a cluster. Having the possibility of getting access to a cluster with about 17 processors, 8 variables can be optimised in one iteration step. This is quite faster than calculating all knots what would take 6561 calculations under the same conditions. 3.2 Implementation of optimisation To optimise a vessels hull form, an objective-function is needed, at least the trivial one, minimize resistance, and one or more constrains. min x R n f (t) sub ject to g(t) g min Where f : R n R and g : R n R m. The objective-function f and the constrain g indicates the results given by policy-functions t. The policy-functions t(v) are the strategy-driven transformation functions used by ARGO with the free variable v. For implementation, the objective-function is set to be the ratio of vessel s resistance and deplacement. This resistance to weight ratio is similar to the power to weight ratio often used in comparison of different motor vehicles. The main advantage in using resistance to power ratios is the possibility of comparing different variations having not the same weight. Having two variations concerning the same resistance, the larger variation is the more efficient one. This extra deplacement can be used for other variations in further transformations. f (t)= RT(t) (t) The constraint displacement has to be above limiting deplacement. It can be solved easily with the calculations done for the objective-function before. g(t)= n (t i ) n min i=1 The free variables of the transformation functions t(v) have to be kept in a realistic limit of giving calculatable results. In this case they have to be configurated during the optimisation process. 3.3 Presentation of results v min v i v max Two transformation functions are chosen for testing the optimisation process. Changing bilge radius will come to a high variation in deplacement and variations in transom immersion lead to changes in wave resistance of the longitudinal waves. For the first runs, no constraint is chosen. Upper and lower boundaries of the free variables were set in performing feasible results in calculations. The variation in 526

5 Type of transformation initial minimum maximum result Bilge radius 5.750m 2.0m 7.0m 5.000m Transom immersion 1.135m m 1.135m -0.25m Table I: Boundaries of the chosen free variables Iteration Bilge Radius Transom Immersion RT/DISPL pred RT/DISPL calc 1 4.9m -0.01m m -0.50m m -0.25m Table II: Iteration steps using bilge radius and transom immersion transformations bilge radius is set to be in the limits between 2.00 m and 7.00 m, the transom immersion varies between 1.0 m below CWL and m above. At first, only three iterations were chosen to show the calculation system s functionality and a calculation system with three calculation points was chosen in development process. In Fig.3 the results are shown. The first iteration in bilge radius is approximately satisfying, but increases with the following iterations in interaction to the transom immersion. The plots of transom immersion show no major change in the iteration s result, only the optimum position varies. To find the optimum, a decrease in the step size of the search interval was implemented. Optimisation of bilge radius Optimisation of transom immersion Iteration 1 Iteration 2 Iteration 3 Result Iteration 1 Iteration 2 Iteration 3 Result RT/Displ RT/Displ Bilge radius Transom immersion Fig.3: Optimisation process of bilge radius( left) and transom immersion (right) Comparing the initial hull form and the variation after three iterations, the advantage in reducing the vessels resistance is only about 11%, table III. On the other hand, the vessel s deplacement increase by about 600t. This extra deplacement can be treated as an indirect resistance reduction, due to the fact that the deplacement can be used in next optimisation step, for example to reduce the vessel s draft. The graphical presentation of initial and final hull form shown in fig. 4, shows the reduction of the wave heigths. In the stern wave system, the decrease in wave can be clearly seen and the result is plausiblewith Vessel Displ.[t] RT[kN] RT/DISPL [kn/m 3 ] Initial hull form Final hull form Table III: Results given by the optimisation after 3 iterations. 527

6 respect to the transom modification. Fig.4: Presentation of CFD-Results, left: Initial calculation, right: final result 3.4 Evaluation of needed calculation points For the evaluation in need of calculation points, the bilge radius calculation was done with an increasing number of calculation points. The plot in fig. 5 shows that the use of only three calculation gives a result more ore less besides the graph with 16 points. Using only one more calculation point will increase the calculation quality and by use of eight points, the graphs plot shows a good correlation to the graph with with 16 points used Setting up calculation points 3 points 4 points 8 points 16 points RT/Displ Bilge radius Fig.5: Influence in calculating with different numbers of calculation points, 3, 4, 8 and 16 points Using 16 or more calculation points seems not do be useful because to many local extrema are generated. Setting up optimisation systems under use of four to eight calculation points smoothes the original function in a useful way. An other advantage of using more than three calculation points leads to the fact that the whole variable interval can be kept and no decrease in step size has to be done in the iteration steps. Also the number of used iteration steps can be kept on a low level contrary to the three point calculations. 4 Conclusions The system s functionality allows a good practical optimisation with the first implemented transformation functions. Further tests have to be done to evaluate the necessary number of calculation points and 528

7 iterations. Further more useful transformation functions need to be implemented to increase the existing library. Preconfigured combination of functions should be available and new combinations have to be saved to be used again. A debug system has to be implemented for use while the optimisation process is running. This is important if calculations lead to results obviously not correct. In this case new calculation points or boundaries have to be set up manually without the need to restart the whole optimising process. References BOYD, S.; VANDENBERGHE, L. (2004), Convex Optimization, Cambridge University Press GOULD, N.I.M.; LEYFFER, S. (2002), An introduction to algorithms for nonlinear optimization, Oxfordshire KNOP, R.; RABIEN, U. (1981), Transformation von Schiffsformen im Vorentwurfsstadium, Gebrauchsanleitung für das Programm APRESS, ESS Nr. 42, TU Hannover KRÜGER, S. (2003), The role of IT in shipbuilding, 2 nd Int. Conf. Computer and IT Applic. Mar. Ind. (COMPIT), Hamburg ABELS, W. (2005), Combining object-oriented and procedural programming in software, 4 nd Int. Conf. Computer and IT Applic. Mar. Ind. (COMPIT), Hamburg, pp SÖDING, H. (1983), Chwarismi I und II, Compiler für technische Entwurfsprobleme, IFS report Nr.15, Univ. Hamburg SÖDING, H. (1999), Das Wellenwiderstands-Programmsystem Kelvin, IfS report 529