Operating Conditions Aligned Ship Design and Evaluation

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1 First International Symposium on Marine Propulsors smp 09, Trondheim, Norway, June 2009 Operating Conditions Aligned Ship Design and Evaluation Lars Greitsch, Georg Eljardt, Stefan Krueger Hamburg University of Technology (TUHH), Hamburg, Germany ABSTRACT This paper discusses a newly developed approach to ship design. It employs Monte Carlo simulations in order to reproduce and prognosticate lifetime operation conditions of a projected (or existing) vessel. On basis of statistical environmental data in combination with direct calculations of the vessel s propulsion it is possible to benchmark different designs regarding e.g. fuel efficiency and rudder cavitation. After the vessel s operating condition (drafts and speed) and the environmental conditions (wind and sea state) are determined, by applying the Monte-Carlo-Method, the corresponding equilibrium condition for each propulsion point is computed by utilising an already implemented manoeuvring algorithm. Following this procedure, it is possible to identify the specific requirement profile and to align the vessel s design with this profile. Since this methodology computes fairly fast, it offers the possibility to perform an optimisation analysis and to qualitatively assess the impact of design variations economically and ecologically. This assessment can be adjusted to different vessel types, shipping routes and connected to this the commodity flow, tailored to the customer s specific needs. In order to validate the calculation method s feasibility, the algorithm s results have been checked against measured long-term data from various vessels in operation. In addition to the power demand as one optimisation parameter, each manoeuvring situation lead to a specific flow condition around the rudder which results directly from the required rudder angle for the task of course keeping. On basis of the determined vessel speeds and rudder angles, the cavitation distribution on the rudder can be estimated. Therefor the flow around the rudder geometry is calculated for all combinations of the prognosticated rudder angles and ship speeds, considering the propeller load resulting from the ships resistance, its floating condition and the wake field. The occurrence of cavitation for each situation is weighted by the relative frequency of the operation condition. Thus the implemented method provides a prognosis of the cavitation risk distribution on the rudder considering the complete operational profile. Now it is possible to evaluate different rudder designs for the vessel on the basis of differences in the cavitation risk. Keywords Ship Design, Propulsion, Operational Profile, Monte-Carlo Simulations, Manoeuvring Simulations, Rudder Cavitation 1 INTRODUCTION The costumer requirements regarding a new ship design went up considerable in the last years. Contrary to that, the methods for benchmarking the new development are still focused on only few operating points (if not just only one). In order to obtain a more detailed view on the different and often diverging design issues it is important to benchmark several design steps with respect to the operational profile of the projected vessel. The intent of the presented approach is to acquire this information. This is done on basis of speed, load case and the weather conditions profiles for the desired route. Subsequently it is possible to evaluate existing and optimize projected designs with respect to various aspects, such as e.g. hull form layout, interaction of hull, propeller and rudder, etc. 2 OPERATIONAL PROFILE The operational profile for the investigated ferry was determined during the regular service in the North Sea within a time period of 11 months. The data for floating condition is observed once per day, the other operational parameters have been averaged from measurements with a sampling rate of 1 second to one value for each half an hour. The speed profile of the investigated vessel is shown in figure 1. Figure 1: Frequency distribution of ship speeds

2 The distribution shows that the vessel sails most of the time with average speed values about 20 percent below design speed and that there is a small accumulation of occurred vessel speeds in the range of 30 percent design speed, which indicates slow speed manoeuvring during the estuary trading. 2.1 Environmental Data Depending on the designated route, the expected weather can be rather different. In order to simulate the resulting added resistances as correct as possible, it is important to gather the necessary data. This can either be done by observation (e.g. during the operation of similar vessels) or the data can be attained from hindcast weather reports. For the presented case, both ways have been employed. The wind force and the angle of attack (aoa) were recorded after observation, whereas the sea state and the correlation of wave height and period were hindcasted. The data was collected and averaged over a period of 10 years from 1990 to 1999 by the GKSS Research Centre. It was provided in the course of the research project ADOPT ( Figure 2 shows the data points and the symbolic path of the vessel s route across the Skagerrak and the North Sea between Gothenburg and Gent. Figure 3: Cumulated distributions - average wave height H 1/3 Worldwide sea state data can be obtained from Soeding (Soeding, 2001). Both parameters wind and sea state are correlated. This dependency has to be acknowledged when applying the subsequently described MontePropalgorithm. During another analysis, concerning an 8200-TEU-vessel, it proved to be feasible to establish the correlation through the following proceeding. At first, the wind force in Beaufort is determined as a floating point number. The sea state is derived afterwards by simply reducing the Beaufort number with a constant subtrahend of 1. For the described vessel and its voyage profile this procedure is slightly suboptimal, since the wind force s statistical spread is wider than the sea state s one, q.v. figure 4. Figure 2: Route of investigated ferry and corresponding data points Since the highlighted points along the route are rather equidistantly distributed, they have been taken into account with equal weighting. This has been done in order to determine one averaged cumulative density function for each weather parameter. Representatively figure 3 shows the individual and the averaged distributions. Figure 4: Comparison of Sea State and Reduced Wind Force (BF orig 1) Further analysis will be carried out in order to improve the correlation.

3 2.2 Data Analysis Before implementing the algorithm the determined data has been analyzed regarding the extent of correlation between the parameters. The extent is specified in terms of a correlation factor. It can take values between -1.0 and 1.0, where small factors near 0 indicate a low grade of correlation and values near 1 respectively near -1 stand for strongly correlated data. In the present work Kendall s correlation factor τ has been chosen, because it is insensitive against outliers and suitable for huge data volumes (Kendall, 1970). Table 1: Correlation factors of Measured Data Compared Parameter Kendall s τ Vessel speed vs. heading Heading vs. wind speed Wind speed vs. wind direction MONTE CARLO METHOD The Monte Carlo Simulation is a statistical method. The presented approach uses the Monte Carlo Algorithm for inversely reproducing a previously determined cumulative distribution function (e.g. for vessel speed). The basis of this algorithm is a large amount of uniformly distributed random numbers between 0 and 1. Each diced random number leads to an abscissa value for the requested operational parameter (figure 5). Figure 6: Distribution quality depending on sample number for the complete system. In the present case the consequences are the revolution speed of the propeller, the propeller pitch, the propeller thrust, the rudder angle for course keeping and the power demand. These propulsion and manoeuvring parameters are determined by calculating the equilibrium condition for each operation point. 4 MONTE-PROP ALGORITHM Figure 7 gives an overview of the program cycle: Figure 5: Scheme of determining the speeds The quality of the reproduced cumulative distribution function (CDF) depends mainly on the amount of samples (figure 6). A feasible compromise between computing time and satisfactory repeatability of a given distribution is achieved with a number of 2000 samples. The calculation on a mobile PC with two processors takes about 18 minutes. Thus by implementing this statistical approach it is possible to generate a relation between a statistical distribution, e.g. the frequency distributions of vessel speed, drafts or weather conditions, and the direct calculated consequences Figure 7: Flowchart of MonteProp-algorithm Starting with an existing ship design, the best matching input data have to be selected. Applying the Monte Carlo Method (see chapter 4), all necessary vessel-specific and environmental parameters are determined for a given sample number. Depending on the voyage profile s characteristics 2000 up to 3000 samples proved to be a reasonable compromise between achieved accuracy and computing time. For each generated operating point, the propulsion s equilibrium condition is simulated, using already implemented manoeuvring algorithms. The Stillwater resistance is determined according to Eljardt (Eljardt, 2006). Additional resistances, resulting from environmental and vessel-specific parameters are acknowledged according to

4 the scheme, developed at TUHH by Eljardt, Greitsch & Mazza (Eljardt et al., 2009). On a standard mobile computer (2 GHz Dual-Core CPU, 4.0GB RAM) simulation with 2000 samples takes scarcely 18 minutes. 5 COMPUTATION OF EQUILIBRIUM CONDITION The diced operating points are computed by use of a manoeuvring algorithm. The algorithm itself has been developed and validated at the TUHH in cooperation with the Flensburger Schiffbaugesellschaft. Detailed information and computed examples are shown in Haack and Krueger (Haack and Krueger, 2004) and Haack (Haack, 2006). It is used within practical manoeuvring simulation for several years. Due to the cooperation with the shipyard the data for the manoeuvring model of the investigated vessel was very detailed. The propulsion plant including the controllable pitch propeller was implemented in the manoeuvring model. The propeller itself is described by means of two-quadrant-diagrams, the possible combinations of shaft speed and propeller pitch are given by the combinator diagram. There are two modes implemented (sea mode and manoeuvring mode), which differ in the gradient of the relation between lever position and pitch setting. The rudder forces for course keeping are acquired from the characteristic diagram of rudder forces and torques. This charcteristic diagram is calculated beforehand with a panel method. More detailed information and an evaluation of the calculated forces are shown in Abels and Greitsch (Abels and Greitsch, 2008) Figure 9: Cumulative Distribution of Propeller Pitch The pitch distributions (figures 8 and 9) show that the presetting of the combinator diagram is reproduced correctly. Most of the time the pitch is set to nearly 100 % design pitch. For the calculation the sea mode is chosen. The simulated pitch distribution is in line with the measured pitch distribution. Figure 10 and 11 show the frequency distribution and the cumulative distribution of the measured and calculated propeller revolution speeds. The simulation fits reasonably well to the measured operation data. The characteristic of the requested speed profile is mirrored in the propeller rpm s distribution. 6 EVALUATION OF THE PROPULSION SIMULATION For evaluating the propulsion simulation and the manoeuvring model of the vessel, the measured and calculated operation data are shown in figures 8 to 13. Figure 10: Frequency Distribution of propeller rpm Figure 8: Frequency Distribution of Propeller Pitch Figure 11: Cumulative Distribution of propeller rpm

5 That indicates a correct transfer of the environmental influence on the propulsion plant within the statistical viewing. The revolution speed demand for the propulsion situations reproduce the observed distribution. In combination with the propeller pitch the calculation of propeller thrust and shaft power is possible. As propeller thrust and shaft power were not measured a direct evaluation of these parameters is not possible. Figures 12 and 13 show the frequency distribution and the cumulative distribution of the measured and calculated rudder angle. 7 CAVITATION RISK ANALYSIS The cavitation risk for the rudder design is calculated as a risk distribution on the surface area of the rudder. For each discretized panel there is the calculated probability of the occurrence of cavitation within the whole operational profile. The cavitation prognosis is carried out with a panel code based on the potential flow theory. This allows very fast calculations and therefore the analysis of the large number of observed operation cases in a finite time period. The used CFD code takes into account the wake field of the observed vessel and the propeller slipstream, which is calculated with the lifting line method. The cavitation is calculated by comparing the local pressure with the vapour pressure of the passing water at the observed location. It is not distinguished between higher and lower pressure gradients. The interpretation of the results is carried out by a cavitation coefficient c cav as a saltus function which has the value 0 for non-cavitating situations of this panel and the value 1 in case of cavitation on the observed panel. In order to benchmark the cavitation risk for different regions on the rudder the cavitation occurrence on each panel is weighted by the frequency of the operation situation. Regarding to the extent of correlation (see: 2.2) the operation points are generated by free combinations of rudder angles δ with strict pairs of vessel speed v s and propeller thrust T. Figure 12: Frequency Distribution of Rudder Angle Table 2: Correlation factors of Input Data Compared Parameter Kendall s τ Vessel speed vs. propeller RPM 0,97 Vessel speed vs. propeller pitch 0,89 Vessel speed vs. propeller thrust 0,94 Vessel speed vs. rudder angle -0,11 This leads to a safety against cavitation S cav for each panel m n S cav = 1 (c cav,i,j f(δ i ) f(v s,j, T j )) (1) i=1 j=1 Figure 13: Cumulative Distribution of Rudder Angle Along with the vessel speed and the corresponding propeller thrust the input paramter for further calculations are calculated. As one example in section 7 the benchmarking of rudder designs by means of the cavitation risk is given. A value of S cav = 1 specifies a 100 percent safety against cavitation for the observed panel in the range of operation situations. Resulting from the saltus function there can be no safety greater than 1. In the same manner a value of S cav = 0 indicates, that the observed panel would cavitate in all operation situations. On basis of the cavitation risk distribution the benefit of a new rudder design can be evaluated directly. The capability of this approach has been presented at NuTTS (Greitsch, 2008). For two different design steps of twisted rudders the cavitation risk distributions are shown in figures 14 and 15. The two versions differ in the twist angle distribution along the rudder heights. Version B shows a cavitation safety of

6 80 percent, whereas the cavitation safety of version A is only 60 percent. Figure 14: Cavitation Safety Distribution Rudder A conditions. That means by existence of an adequatly detailed simulation model of the examined vessel, its performance in operation can be estimated and evaluated. So e.g. the consequences of design changes on fuel efficiency, course keeping demand or rudder cavitation can be prognosticated. REFERENCES Abels, W. and Greitsch, L. (2008). Using a bridge simulator during the early design-stage for evaluation of ship design manoeuvring ability. In Proceedings of the 7th International Conference on Computer Applications and Information Technology in the Maritime Industries, Liege, Belgium. Eljardt, G. (2006). Development of a Fuel Oil Consumption Monitoring System. Diploma Thesis, Hamburg University of Technology. Eljardt, G., Greitsch, L., and Mazza, G. (2009). Operation-based ship design and evaluation. In International Maritime Design Conference, Trondheim, Norway. Greitsch, L. (2008). Prognosis of rudder cavitation risk in ship operation. In Numerical Towing Tank Symposium, Brest, France. Haack, T. (2006). Simulation des Manoevrierverhaltens von Schiffen unter besonderer Beruecksichtigung der Antriebsanlage. Dissertation, Schriftenreihe Schiffbau, Hamburg. Figure 15: Cavitation Safety Distribution Rudder B 8 CONCLUSIONS A route based ship design procedure has been developed. It allows the estimation of the propulsion and manoeuvring conditions within the whole operational profile of a projected or already existing vessel only on the basis of preset distributions of vessel speed and loading and weather Haack, T. and Krueger, S. (2004). Propulsion plant models for nautical manoevre simulations. In Proceedings of the 3rd International Conference on Computer Applications and Information Technology in the Maritime Industries, Madrid, Spain. Kendall, M. G. (1970). Rank Correlation Methods. Griffin, London. Soeding, H. (2001). Global Seaway Statistics. Schriftenreihe Schiffbau, Hamburg.