Experimental study of the resistance of a hydrofoil supported watercraft (hysuwac)

. A possible alternative to reduce fuel consumption on a ship is through energy efficiency. For this purpose, a hydrofoil supported watercraft (hysuwac) utilizes two hydrofoils, one installed near the bow and the other near the stern of the catamaran, to reduce the vessel’s resistance. To investigate the effectiveness of the hydrofoils, CFD calculations were conducted in an earlier study. The purpose of this study is to provide experimental data to validate the CFD calculation results reported earlier for which towing tests were conducted at the Laboratory of Ship Hydrodynamics, ITS Surabaya, Indonesia. The ship model was made by using a three-dimensional print, which is then assembled into a ship model that meets the test requirements. The hydrofoil used has a NACA 64 1 -212 section with an angle of attack of 4°. Twelve variations of towing tests were carried out with six variations of speed and two conditions, namely catamaran without and with foil system. A comparison between the CFD and experimental results shows that the CFD results are consistent with the experimental data. The minimum magnitude of percentage difference between the CFD results and experimental data is 1.14%, while the maximum magnitude of this is 16.79%. The observed difference is ascribed mainly to scale effects.


Introduction
As 80% of world cargo is transported by ships, efforts have been made to reduce the ship fuel consumption so as to minimize the green-house gas (GHG) emissions.One effort is to increase the energy efficiency of a vessel through reduction of the vessel's resistance.A hydrofoil supported watercraft (hysuwac) utilizes two hydrofoils, one installed near the bow and the other near the stern of the vessel, to reduce the vessel's resistance.To investigate the effectiveness of the hydrofoil system in reducing the vessel's resistance, CFD calculations were carried out in an earlier study and the results were reported by Suastika et al. [1].
The accuracy of CFD results depends on the accuracy of modeling the underlying physical phenomena and its numerical implementation in the CFD code.Verification and validation (V & V) of CFD results refer to the assessments of the above-mentioned accuracy of physical modeling and numerical implementation.Verification can be viewed as an assessment on whether the equations implemented in the CFD code are solved correctly, while validation can be viewed as an assessment on whether the correct equations have been solved, that is, the equations which model the underlying physical phenomena [2].
A verification assessment may include, e.g., a check of the discretization error or a quantification of a numerical diffusion [3].A recommended method for a verification assessment of CFD results is to compare them with highly accurate analytical results.In many instances, by lacking analytical results, this is done by doing a grid sensitivity study.In this regard, Roache [4] introduced the grid convergence index (GCI) for the uniform reporting of grid refinement studies.On the other hand, to assess the correctness of the physical modeling in a validation assessment, CFD calculation results are usually compared with accurate benchmark experimental data.Some physical models implemented in CFD include, for example, the conservation principles of mass, momentum, and energy, modeling the turbulent characters of a flow, or a physical model for a multiphase flow.
Several V & V studies were reported in the literature.Vos [5] performed V & V of CFD data for the construction of flight simulations.Mancini [6] performed V & V of CFD simulations of planing high speed crafts.In the application of CFD in the field of ship hydrodynamics, it is well-known that results of CFD calculations for planing crafts are less reliable than displacement ships.Lee [7] reported trend validation of CFD calculation results.Further, there are uncertainties in the conversion from model-scale to full-scale results.A guideline for uncertainty analysis in CFD verification and validation is given by the ITTC [8].
The purpose of this study is to provide experimental data to be used to validate the CFD calculation results of the resistance of a hydrofoil supported watercraft (hysuwac) reported earlier by Suastika et al. [1].In their study, a foil system was retrofitted to an existing catamaran and its effects on the vessel's resistance was investigated by conducting CFD simulations.Verifications of the CFD results have been carried out by performing grid independence tests, variation in the number of iterations, and variation of the time step used in the simulations.However, a validation assessment of the CFD results has not been carried out.

Methodology
To provide the experimental data, model tests were carried out in the towing tank of the Laboratory of Ship Hydrodynamics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia.The dimensions of the towing tank are 50 m long and 3 m wide.It allows for a maximum water depth of 2 m.The ship particulars and the foil dimensions are summarized in Table 1.The resistance tests were conducted in accordance with the ITTC guideline [9,10].In the experiments, the total resistance was measured by using a load cell.The data obtained from the model tests were subsequently converted to a full-scale ship resistance by using the ITTC 1957 method [11].For the validation assessment, the scale-up experimental data of total ship resistance (referred to as EFD data) are compared with the full-scale CFD calculation results of Suastika et al. [1] (referred to as CFD data).

Preparation of the test model
The ship model was prepared in accordance to the ITTC procedure [9,10].The dimensions of the model were determined by considering the maximum allowable speed of the carriage of the towing tank, which is approximately 3 m/s.Further constraints are imposed by the dimensions of the prototype, particularly the overall length of the vessel (LOA) which is 10.5 m.Based on the above constraints, a test model was made with a geometrical scale of one upon twenty-six dot two five (λ = 1/26.25).This results in a length of the model of 0.4 m.The other dimensions of the ship model and the prototype are summarized in Table 2.The hydrofoil used has NACA 641-212 section with an angle of attack of 4°.Froude similarity was applied between the model and the prototype, that is, the Froude number of the model is equal to the Froude number of the prototype: where the subscripts m and p refer to model and prototype, respectively.The Froude number in Eq. ( 1) is initially calculated as: where V is the speed, L is the vessel's overall length (LOA), and g is the gravitational acceleration.The maximum Froude number according to Eq. ( 2) is 1.1, corresponding to a prototype speed of 21.5 knots.In Section 3, the Froude number will be recalculated because of the significant change of the wetted surface area (WSA) and the water line of the vessel as it moves on the water.The significant change of vessel's WSA and water line affect the vessel's resistance significantly.
The model was manufactured by using a 3-D printer.Figure 1a shows the file to be printed in the 3-D printer while Figure 1b shows the resulting ship model after finishing for the case without foil system.Figure 2 shows the positioning of the foil below the water surface, which follows the recommendation of the 1986 United States Patent No. 4,606,291 specifying that the ratio of foil depth measured from the water surface to the foil chord (h/c) is 0.4.The front foil is placed at 30% LOA, measured from the LCG (longitudinal center of gravity) to the trailing edge of the front foil.The rear foil is placed at 54% LOA, measured from the leading edge of the front foil to the leading edge of the rear foil.Figures 3a and b show photographs while the model was towed in the towing tank for the cases of catamaran without and with foil system, respectively.

Measurement Program
Table 3 summarizes the measurement program of the towing tank tests carried out in this study.Two conditions were tested, namely catamaran without and with foil system, for which six speeds were measured for each condition.The prototype speed as well as the model speed, including the corresponding Froude number are listed in Table 3.

Conversion from model-scale to full-scale resistance
The CFD calculations reported by Suastika et al. [1] were done for a full-scale vessel while the laboratory experiments were done at a model scale.Therefore, it is necessary to convert the model-scale results to full-scale results.
In the experiments the total resistance of the vessel was measured at different speeds.The coefficient of total resistance for the model CT;m is calculated as: where m is the mass density of the water used in the experiments, Vm is the speed of the model and Sm is the wetted surface area of the model.
Conversion to the total resistance of the prototype CT;s (full scale) was done in accordance to the procedure given by the ITTC 1957 [11].The coefficient of total resistance of the ship CT;s is calculated as follows: where CF;s is the coefficient of skin friction of the prototype, CR;s is the coefficient of residual resistance of the prototype and CA is a coefficient of allowance (CA = 0.0004).The residual coefficient of the prototype CR;s is assumed to be equal as the residual coefficient of the model CR;m, which can be obtained from the experiments (CR;s = CR;m).The coefficient of residual resistance of the model CR;m is calculated as follows: The coefficient of skin friction CF, both for the model and the prototype, is calculated using the ITTC correlation line: where Re is the Reynolds number, using respectively the model Reynolds number for the calculation of CF;m and the prototype Reynolds number for the calculation of CF;s.The Reynolds number is defined as: where V is the vessel speed, L is the length of the vessel and  is the kinematic viscosity of the water.

Results and Discussion
Both the CFD and experimental results showed that there is a significant change of the vessel's WSA as the vessel moves on the water surface, particularly at relatively high speed.
For the above reason, the Froude number given in Eq. ( 2) was recalculated by using the square root of the WSA as a parameter for the length scale instead of the vessel's length as follows: where S is the vessel's WSA.The values of WSA used in the calculation of Eq. ( 8) were those calculated using CFD as reported in Suastika et al. [1].The results of total resistance as function of Froude number Fr are plotted in Figure 4, in which a comparison is made between the CFD and model test results for the cases of catamaran without and with foil system.Figure 4 shows that the trend of the CFD results is in good agreement with that of the experimental data.The application of the foil system decreased the total resistance at Fr larger than approximately 0.78 but increased the total resistance at Fr < 0.78.In general, there is a good agreement between the CFD results and experimental data.To quantify the difference between the CFD and experimental results, the percentage difference between these were calculated.Tables 4 and 5 summarize the percentage difference between the CFD and experimental results of total resistance for the cases of catamaran without and with foil system, respectively.The percentage difference ET is calculated as follows: where RT;CFD is the total resistance calculated using CFD and RT;EFD is the total resistance obtained from the experiments.The percentage discrepancy between CFD and experimental data has a minimum magnitude of 1.14% and a maximum magnitude of 16.79%.The discrepancy is primarily due to scale effects.Scale effects occur when the model's force ratios are not equal to the prototype's force ratios, resulting in differences between the up-scaled model and prototype observations [12,13].More particular, while the model and prototype have the same Froude values, their Reynolds numbers are not.The prototype's Reynolds number is hundreds of times greater than the test model's Reynolds number.

Conclusions
Towing tank tests were carried out to generate resistance data for a hydrofoil assisted watercraft (hysuwac).The information was used to confirm the findings of CFD simulations published in an earlier work [1].The trend of the CFD findings is consistent with the pattern of the experimental data.Further comparisons of the experimental data and the CFD findings reveal that the CFD results agree with the experimental data.The foil method reduced total resistance at Froude numbers greater than about 0.78 but increased total resistance at Fr 0.78.The minimum magnitude of percentage difference between the CFD results and experimental data is 1.14%, while the maximum magnitude of this is 16.79%.The observed difference is ascribed mainly to scale effects.

Fig. 1 .
Fig. 1.The file to be printed in a 3-D printer (a) and the resulting catamaran hull model after finishing (b).

Fig. 2 .
Fig. 2. Position of the hydrofoil below the water surface.

Fig. 3 .
Fig. 3.The model being towed in the towing tank at the speed of 21.5 knots (Froude number Fr based on the LOA of 1.1) for the case of catamaran without hydrofoil (a) and catamaran with a foil system (b) showing a bow lift due to the foil system.

FrFig. 4 .
Fig. 4. Comparison of vessel's total resistance as function of Froude number obtained from CFD calculations and towing tank experiments for the cases of catamaran without and with foil system.

Table 1 .
Dimensions of the prototype ship and the foil

Table 2 .
Dimensions and scaling from prototype to test model

Table 4 .
Percentage error between CFD and EFD data for the case of catamaran without foil system

Table 5 .
Percentage error between CFD and EFD data for the case of catamaran with foil system