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Experimental assessment of interference resistance for a Series 60 catamaran in free and fixed trim-sinkage conditions
Ocean Engineering 53 (2012) 38–47
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Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Experimental assessment of interference resistance for a Series 60 catamaran in free and fixed trim-sinkage conditions Antonio Souto-Iglesias n, David Ferna´ndez-Gutie´rrez, Luis Pe´rez-Rojas Model Basin Research Group (CEHINAV), Naval Architecture Department (ETSIN), Technical University of Madrid (UPM), 28040 Madrid, Spain
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 February 2012 Accepted 3 June 2012 Editor-in-Chief: A.I. Incecik
The interference resistance of multihulls taking into account the test condition (fixed or free model) is experimentally studied. Experiments have been carried out with a commercial catamaran model and more extensively with a Series 60 catamaran. The influence of the testing condition (fixed or free) together with the influence of hull separation has been analysed. The relevance of these experimental results in the separation optimisation techniques based on slender body flow solvers is discussed. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Interference resistance Interference factor Series 60 Catamaran Free trim Fixed trim Fixed sinkage Free sinkage Free model Captive model
1. Introduction A significant body of literature analysing multihulls hydrodynamics (Chen et al., 2003; Insel and Molland, 1992; Migali et al., 2001; Molland et al., 1996; Turner and Taplin, 1968; Yeung et al., 2004), mainly considers slender body simplifications and focus on moderate and high speed regimes. Broglia et al. (2011) and Zaghi et al. (2011) use instead a Navier–Stokes solver to simulate multihulls, finding a good agreement for the resistance values and describing complex interference effects at high Froude numbers regimes. Most of these analyses assume a fixed model condition consequently reducing the computational effort. This, combined with the slender body assumption, allows for the simulation of a wider range of configurations in terms of separation and velocity for a reasonable computational effort. With these types of codes, it is therefore feasible to set up a separation optimisation framework in early design phase (Moraes et al., 2007; Yeung and Wan, 2007). In Souto-Iglesias et al. (2007), the interference resistance of multihulls was analysed by assessing its relationship with the n
Corresponding author. Tel.: þ34 913367156; fax: þ34 915442149. E-mail addresses: [email protected] (A. Souto-Iglesias), [email protected] (D. Ferna´ndez-Gutie´rrez), [email protected] (L. Pe´rez-Rojas). 0029-8018/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.oceaneng.2012.06.008
shape and amplitude of the wave train between the hulls for a specific commercial vessel design. The free model condition was then considered making it more difficult to identify interference effects due to substantially different dynamic trims and sinkages between the monohull and the catamaran. This case study is herein revisited by considering the fixed model condition. In addition to the commercial vessel, a Series-60 (S60) catamaran has been experimentally studied. Its hull shape significantly changes from the former, expanding the geometry types analysed. Although the S60 is a well known hull for experimental and computational analyses (Todd, 1964; Kim and Jenkins, 1981; Toda et al., 1988, 1992; Nakatake and Takeshi, 1994; Tarafder and Suzuki, 2008), to the authors’ knowledge, its behaviour as a multihull has not yet been experimentally described and such knowledge may be useful for CFD practitioners working on multihull hydrodynamics. In Yeung et al. (2004) the interference resistance of a S60 catamaran was numerically studied neglecting trim and sinkage influences. They provided the value of the interference factor for a wide range of separations and speeds and a significant insight into the complexity of the multihull wave interference phenomena. Their predictions have been contrasted with experimental results in the present paper. The paper is organised as follows: first, aiming at presenting the problem and the notation, the interference resistance is defined. Second, the commercial vessel case that was studied
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mh
Nomenclature
n cat cF cT cw Dzbow Dzstern g Fn IF L
catamaran friction resistance coefficient total resistance coefficient wave resistance coefficient variation of bow draft in free model condition (m) variation of stern draft in free model condition (m) gravity (m/s2) Froude number interference factor length between perpendiculars (m)
under the free trim condition in Souto-Iglesias et al. (2007) is revisited, this time, considering the fixed trim condition effect on interference resistance. Third, a S60 catamaran is analysed comparing the experimental data under fixed and free trim test conditions with the existing data found in the previously mentioned literature. Finally, a summary of the drawn conclusions together with future works are provided.
2. Interference resistance
RWcat 2RWmh 2RWmh
ð1Þ
Ideally, the value of the interference factor should be kept as small as possible, negative if achievable (Yeung and Wan, 2007). To correctly calculate the interference factor, the friction resistance has to be subtracted from the total resistance obtained in the experiments. Air drag and correlation allowance are considered negligible in the present analysis. The wave resistance is obtained via the Hughes (Lunde et al., 1966) decomposition. RT ¼ RW þ ð1þ kÞRF
ð2Þ
where k is the form factor, assumed identical for both the monohull and the catamaran cases. RF is the friction resistance of a flat plate with equivalent wetted surface, computed from the friction drag coefficient (CF) obtained via the ITTC 1957 correlation line formula: cF ¼
0:075 ðlog10 ðRe2ÞÞ2
monohull kinematic viscosity (m2/s) flat plate friction resistance (N) total resistance (N) wave resistance (N) wave resistance of monohull (N) wave resistance of catamaran (N) Reynolds number Series 60 separation (m) velocity (m/s)
wave resistance implies changing the denominator of Eq. (1) to the total resistance, since as aforementioned, friction components cancel out in the numerator. The value of the interference factor is investigated in the present paper by looking at the influence of the testing condition for two vessels, namely a commercial vessel and a Series 60 (S60). The characteristics of both models are presented in Table 1.
3. Commercial vessel
In multihulls, there is usually a strong interference between the wave systems generated by each hull. This interference can either be favourable or unfavourable to the global resistance of the hull. To properly characterise this effect, the interference factor IF is defined as the ratio of the difference between the wave resistance of the catamaran, RWcat , and twice the wave resistance force of a monohull, RWmh : IF ¼
RF RT Rw RWmh RWcat Re S60 s V
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3.1. General This vessel is commonly used in the transport of goods and fish to and from a sea farm. The main dimensions of the model are presented in Table 1. The reference system considered, the notations describing the hull separation and the vessel geometry are shown in Fig. 1. The separation (s) is defined as the distance between each hull’s centreline, and is made nondimensional with the length between perpendiculars (s/L). The free model condition studied in Souto-Iglesias et al. (2007) was aimed at finding the relationship between the interference factor Table 1 Main dimensions of the case studies. Main features
Commercial vessel
S60
Units
Length between perpendiculars (L) Beam (mh) Draft Wetted surface (mh) Displacement (mh) Block coefficient Length–beam ratio Beam–draft ratio
2.208 0.238 0.120 0.885 84.35 0.653 9.28 1.98
2.500 0.333 0.133 1.062 65.70 0.600 7.51 2.50
m m m m2 kg
ð3Þ
There is a strong dependence between the wave resistance and the value set for the form factor. This significantly affects the extrapolation procedure but moderately influences the value of the interference factor IF while maintaining its sign, the reason being that the frictional components of the resistance cancel out in the numerator of Eq. (1). Therefore, establishing whether the interference effects are favourable or unfavourable does not depend on eventual uncertainties of the form factor computation procedure. The interference factor is sometimes defined considering the total resistance (Zaghi et al., 2011). According to the Hughes resistance decomposition, using the total resistance instead of the
Fig. 1. Commercial vessel model geometry and reference system.
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and the amplitude of the wave system in between the two hulls. The present study completes the previously mentioned work by performing tests in fixed model condition using this geometry, thus eliminating the effects of sinkage and trim movements. A photograph taken during the tests of this paper’s experimental campaign is shown in Fig. 2. Further information about this hull is included in Souto-Iglesias et al. (2007) including its 3D geometrical definition as an IGES file, provided as a supplementary material. The following tests were carried out:
Monohull, free model Monohull, fixed model Catamaran, s/L¼ 0.388, in free model condition Catamaran, s/L¼ 0.388, in fixed model condition
The separation (s/L¼0.388) was chosen for having the most interesting interference effects, as found in Souto-Iglesias et al. (2007). A test matrix comprising of the speeds shown in Table 2 was initially devised. The speed range of main interest corresponds to Froude numbers between 0.2 and 0.4. For the Froude number 0.375 the experiment was repeated 5 times in order to assure that measurement uncertainties remain considerably smaller than the interference effects to analyse. A collection of extra velocities was run for the range 0.3 oFno0.4 in order to
Fig. 2. Picture of commercial vessel-model test.
Table 2 Froude numbers and velocities considered for the commercial vessel tests. Point
Fn
V (m/s)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0.100 0.150 0.200 0.250 0.300 0.350 0.375 0.375 0.375 0.375 0.375 0.400 0.450 0.500 0.550
0.465 0.698 0.931 1.164 1.396 1.629 1.745 1.745 1.745 1.745 1.745 1.862 2.094 2.327 2.560
properly characterise the resistance hump. Videos of these experiments, provided as supplementary material, can be found online at http://canal.etsin.upm.es/ftp/2012/S60/ 3.2. Results The resulting experimental curves are presented in Fig. 3. It can be observed that there is a significant difference in the results for the fixed and free model conditions, with the free model resistance being larger than the fixed model in all cases, as in Kim and Jenkins (1981) for a S60 monohull and Moraes et al. (2004) for the Wigley hull. With regard to the differences between monohull and catamaran, the tendency in the monohull resistance is monotonic whilst a clear hump can be appreciated for the catamaran configuration. Focusing on the hump region, these characteristics are discussed in detail in what follows next. In order to adequately estimate the interference factor for a continuous range of Froude numbers, the resistance curves were fitted with NURBS (Fig. 4 left and right). In these figures, the markers correspond to the raw experimental data. The interference factor refers to a comparison between wave resistances which have been obtained from the total resistance following the procedure described in Section 2 and considering a form factor of 0.24. The form factor has been taken as the same for the catamaran and the monohull. Fig. 4 left and right show the differences in wave and total resistance in the hump region (0.3oFno0.4) between the monohull and the catamaran for the free and fixed model conditions respectively. It can be seen that the wave resistance and the total resistance follow a similar trend, although as previously mentioned, the values remain lower for the fixed trim condition. Favourable interference regions corresponding to those where the catamaran resistance is smaller than twice that of the monohull can also be observed. The interference factor is calculated from these data with the results shown in Fig. 5. While it is apparent that the values are different for 0.3 oFno0.34, a very similar pattern is obtained for Fn40.34. Overall, the tendency of the interference factors for the free and fixed model conditions is similar, with some differences in the IF values for the Froude numbers between 0.3 and 0.34. This fits with what was expected from analysing the trim angles of the monohull and catamaran configurations in free model condition, as discussed in Souto-Iglesias et al. (2007). Results regarding sinkage and trim are presented in Fig. 6. They are made nondimensional using the typical length V2/g (Eqs. (4) and (5)), as in Kim and Jenkins (1981). Trim ¼ ðDzbow Dzstern Þ2g=V 2
ð4Þ
Sinkage ¼ ðDzbow þ Dzstern Þg=V 2
ð5Þ
Fig. 3. Total resistance of commercial vessel, s/L¼ 0.388.
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Fig. 4. Total and wave resistance, commercial vessel, free (left) and fixed (right) conditions.
Fig. 5. IF of commercial vessel for test case s/L¼ 0.388. Fig. 7. S60 catamaran model.
Fig. 6. Sinkage and trim, commercial vessel.
This typical length is the characteristic wave length over 2p. Although the sinkage is significant (o10% of the draft), its behaviour is very similar for both the monohull and the catamaran. If we look at the trim, absolute trim angles remain small (between 0.31 and 0.31, equivalent to 70.06 in the nondimensional trim from Fig. 6) with small variations. The trim angle reduction around Fn¼0.37 for the catamaran may help in explaining the favourable interference found in the free model condition for this velocity.
4. Series 60 4.1. General The tests have been carried out with a Series 60 (Todd, 1964) catamaran (fig. 7). The model characteristics have been presented in Table 1 together with those of the commercial vessel test case. The dimension ratios are fairly similar for these two vessels but
Fig. 8. S60 (Todd, 1964) body plan (black) and present study (red). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
the hulls are significantly different: 1. The S60 has no cylindrical section compared to a long one for the commercial vessel. 2. The S60 has a conventional cruise type aft body and the commercial vessel has a transom stern. 3. The S60 has no knuckles while the the commercial vessel has a hard chin. Prior to the milling of the models, the hull geometry was computationally redefined starting from the IGES definition used
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as benchmark in the Tokyo 1994 CFD Workshop. The reason for this refairing is that too many surface patches with not enough quality matching were used in the latter. Furthermore, a vertical extension of the model was required to cope with the generated waves from high Froude number tests. The matching of the updated geometry with the original S60 definition (Todd, 1964) is good, as can be appreciated in Fig. 8. The IGES file used here is provided as a supplementary material at http://canal.etsin.upm. es/ftp/2012/S60/, with the aim to serve as a standard digital definition for further studies. The following separations have been tested: a) b) c) d)
s¼0.565 m, s/L¼0.226 s¼0.768 m, s/L¼0.307 s¼0.971 m, s/L¼0.388 s¼0.1174 m, s/L¼0.470
The rationale behind this selection is that, according to the computational analysis of a Series 60 catamaran by Yeung et al. (2004), s/L¼ 0.226 was determined as the separation ratio for which the largest favourable interferences take place. s/L¼0.388 is the separation ratio with the largest favourable interference effects for the commercial vessel case studied in the previous section. s/L¼0.307 is the mean value of 0.226 and 0.388. s/L¼0.470 is larger than 0.388 and chosen to evenly space the 4 separations. Results are presented and discussed for each of these 4 separations. The form factor used for the computation of the wave component of the resistance is taken as 0.0673. This value was deduced by Min and Kang (2010) who undertook a very thorough study on the dependence between the form factor and the Reynolds number. As for the commercial vessel, it is assumed that the form factor for the monohull and the catamaran is the same. The velocities presented in Table 3 were run for the monohull and for the catamaran with all four separations in both free and fixed model conditions. On top of the points presented in Table 3, a total of 5 extra runs were done for the regions of convexity change in the resistance curves. These extra points are shown in the resistance curves in the next section. Since it was previously
unclear where the strongest interference effects would take place, the range of Froude numbers is wider than the one used for the commercial vessel (Table 2). The videos of these experiments, provided as a supplementary material, can be found online at http://canal.etsin.upm.es/ftp/2012/S60/. A photograph taken during the experiments is presented in Fig. 9.
4.2. Resistance curves for all separations The resistance curves for the monohull and the catamaran with all 4 separations in fixed and free model conditions are presented in Figs. 10 and 11. There is a slight hump in the resistance curves for both fixed and free model conditions for 0.3oFn o0.4. In both conditions and as a general trend, the resistance diminishes as the separation increases, tending to that of the monohull. Let us point out that the monohull resistance has been doubled for the comparison. The translation of these results in the interference factor is later discussed.
Fig. 9. Picture of S60 model test.
Table 3 Froude numbers and velocities for the S60 catamaran tests. Point
Fn
V (m/s)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0.15 0.20 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.45 0.50 0.55
0.743 0.990 1.238 1.288 1.337 1.387 1.436 1.486 1.535 1.585 1.634 1.684 1.733 1.783 1.832 1.882 1.931 1.981 2.030 2.080 2.129 2.229 2.476 2.724
Fig. 10. S60, total resistance in free model condition.
Fig. 11. S60, total resistance in fixed model condition.
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4.3. Resistance curves in free and fixed model conditions The graphs in Fig. 12 show the resistance curves for each separation in fixed and free model conditions, and compare them
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with the monohull ones. As a general trend, it can be observed that the resistance is greater in the free model condition than in the fixed one for each separation. This is best appreciated when comparing the data for the greatest speed. In Section 3.2, a similar effect is described
Fig. 12. S60, total resistance in fixed and free model conditions. Top left: s/L=0.226, Top Right: s/L=0.307, Down left: s/L=0.388, Down Right: s/L=0.470.
Fig. 13. S60, total and wave resistance in free model condition. Top left: s/L=0.226, Top Right: s/L=0.307, Down left: s/L=0.388, Down Right: s/L=0.470.
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for the commercial vessel. As can be appreciated in Fig. 12, the differences are larger for the catamaran than for the monohull and even larger for small separations compared to large ones. This effect was also described for the Wigley hull by Moraes et al. (2004).
For the catamaran in free model condition, with s/L¼0.226, the greatest speeds could not be reached due to the generated waves entering the model. For s/L¼0.307 in free model condition, the planning range for the catamaran configuration is reached.
Fig. 14. S60, total and wave resistance in fixed model condition. Top left: s/L=0.226, Top Right: s/L=0.307, Down left: s/L=0.388, Down Right: s/L=0.470.
Fig. 15. IF for the S60. Top left: s/L=0.226, Top Right: s/L=0.307, Down left: s/L=0.388, Down Right: s/L=0.470.
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This can be deduced by looking at the flattening of the resistance curve for Fn¼0.55. For s/L¼0.388, the difference in resistance values between the monohull and the catamaran grows smaller for large Froude numbers both in fixed and free model conditions. This tendency is made clearer with the largest separation (s/L¼0.470). 4.4. Wave resistance In order to calculate the interference factor for a continuous range of Froude numbers, the resistance curves have been fitted with NURBS. For each case, wave resistances have been obtained from the total resistance following the procedure described in Section 2. The curves representing these results are shown in Figs. 13 and 14 for free and fixed model conditions respectively. In these figures, the markers correspond to the raw experimental data. Data are presented for Fn4 0.3, where the first behaviour differences between the monohull and the catamaran start to take place. We can conclude that for the free model condition and smallest separation, there is no favourable interference region. For the largest Froude numbers the catamaran and the monohull resistances tend to converge. In the mid part of the graphs the trends are more intricate and described through the IF in the next section. 4.5. Interference factor Using the wave resistance curves presented in the previous section, the interference factors for both fixed and free model conditions and for all separations are presented in this section.
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Results are compared with Yeung et al. (2004) and Yeung (2005), who considered a thin-ship potential approximation to model the problem, with a fixed model hypothesis. Interference factors for free and fixed model conditions are presented for all separations in Fig. 15. Focusing on s/L¼0.226, it can be appreciated that the free model and fixed model interference factors are significantly different. Although according to Yeung et al. (2004), where this last separation with Fn¼0.33 produces the most favourable interference effects, this does not occur in the present experiments. For Fn¼ 0.33 the interference is unfavourable and the minimum is shifted to around Fn¼0.38. The free model condition presents overall a more unfavourable behaviour than both fixed condition and theoretical model. This is relevant since in real applications, the free model condition applies. For the largest velocities there is a convergence between the fixed model condition results and those of Yeung et al. (2004). For s/L¼ 0.307, it can be appreciated that the free model interference factor significantly differs from the fixed model one in the range 0.35oFno0.4. With regards to the comparison with Yeung et al. (2004), it is noticeable that the peak value of the interference coefficient is shifted to 0.05 (from 0.38 to 0.43 in the experimental results). This shift is also present in the minimum value of the interference factor. For the largest velocities there is a convergence between the experimental results and those from Yeung et al. (2004) in free and fixed model conditions. Furthermore, the interference effects diminish and the IF tends to zero, as is the case in Zaghi et al. (2011). Analogously to what happened for the commercial vessel, in the S60 case, the strongest favourable interference effects are found for s/L¼0.388. With regards to the comparison with Yeung
Fig. 16. Contour plot as function of Fn and s/L of the IF for the S60. Top: Yeung et al., (2004), Down Right: Free model, Down left: Fixed model.
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et al. (2004), the peaks and valleys in the experiments are delayed with respect to the model. For the largest velocities, the convergence of the experimental results found in this paper to those of Yeung et al. (2004) is clearly appreciated. More attenuated trends are observed for the largest separation, s/L¼ 0.470. An interesting global representation of these effects across the different separations is given. To do this, a contour projection of the 3D graph for the IF is presented in Fig. 16. The tendencies observed in the individual graphs for each separation (Fig. 15) are now clearer. The colour scale in each graph is individualised due to the range of the interference factor data from Yeung et al. (2004) being significantly shorter than the one found experimentally. Globally there are some similitudes in the interference patterns but some differences can be appreciated. Comparing the free model experimental data (which is the realistic configuration to be found in full scale) with those of Yeung et al. (2004) shows that the most favourable interference takes place at a similar Fn (0.33) and with a similar IF (around 0.2) but at a larger separation (0.4 instead of 0.226). This Fn is similar to that found by Zaghi et al. (2011) with a slenderer model. The unfavourable interferences are stronger in the experimental case with a maximum of the order of 0.7 instead of the theoretically calculated 0.3. It is significant that this maximum does not take place for the smallest separation, as is the case in Zaghi et al. (2011). Also, in experiments, there is a smoother transition between the favourable and unfavourable regions compared to the theoretical model. Now comparing free and fixed model condition tests, other differences can be appreciated: 1. The transition between favourable and unfavourable regions is sharper for the fixed model case. Such a sharp transition in the fixed model case is predicted by the theoretical model. 2. For the smallest separations and contrary to what happens in the free model condition, there are favourable, although quite mild, interference regions in the fixed model condition results. 3. Although the unfavourable interference regions are similar in size, the free model ones are more intense. 4. The most favourable interference factor in fixed model condition is smaller than the free model one.
Fig. 17. Sinkage for the S60.
Fig. 18. Trim for the S60.
Looking at the trim (Fig. 18) and in all cases, the differences are more patent for larger Fn. Between Fn¼0.38 and Fn¼0.45 a significant trim increase is appreciated. This shift requires further investigation in order to evaluate a possible relation between differences in the IF in free and fixed model condition.
5. Conclusions Summarizing, the free model condition tends to enhance the favourable and unfavourable interference effects. 4.6. Sinkage and trim The object of this section is to analyse the relationship between the IF differences in free and fixed model conditions and the dynamic position (sinkage and trim) in free model condition. It is also relevant to analyse differences in sinkage and trim in free model condition between the monohull and the catamaran; such values are presented in nondimensional form in Figs. 17 and 18, following the definitions by Kim and Jenkins (1981) presented in Eqs. (4) and (5). When comparing the S60 data with those of the commercial vessel (Fig. 6), sinkage seems to be of the same order but trim is significantly larger for the S60. Pending future work, we believe this may have an influence on the IF behaviour change between fixed and free model conditions. When comparing the S60 monohull and the S60 catamaran in free model condition, large differences in sinkage can be appreciated for 0.3 oFno0.42 (Fig. 17). For the shortest separation (s/L¼0.226) the sinkage for the catamaran is around 50% greater. Also for s/L¼0.226, as can be seen in Fig. 15, the differences in the IF between free and fixed model are significant but not monotonic, unlike the sinkage differences, which are monotonic.
The interference resistance of multihulls taking into account the testing condition (fixed model or free model) has been experimentally studied. Experiments have been carried out with a commercial catamaran model and more extensively with a Series 60 catamaran. For the commercial vessel, the influence of the model condition has been analysed for the separation in which the strongest interference effects take place. In this case it has been shown that the influence of the model condition (freefixed) is not substantial. This is consistent with the experiments presenting moderate dynamic trim-sinkage values and small differences in dynamic trim and sinkage between the monohull and the multihull configuration in free model condition. For the Series 60 model a range of separations has been studied and compared with the fixed model slender body theoretical results. The differences between the free and fixed condition experimental results are significant, with the free condition providing more extreme cases in the favourable and unfavourable interference regimes. The optimum interference factor ( 0.2) appears at a Froude number of 0.33, agreeing with theoretical results. Nonetheless, this optimum interference occurs for a substantially larger separation ratio (0.40) than the theoretically predicted (0.226). The transition between favourable and unfavourable regions is sharper for the fixed model case. Such a sharp transition is in accordance with the theoretical model predictions. For the smallest separation and
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contrary to what happens in the free model condition, there are favourable, although quite mild, interference regions in the fixed model condition. It has been described that for each separation there is a shift in the maximum favourable and unfavourable interference Froude numbers as compared to the theoretical model. In general, the free model condition tends to enhance the favourable and unfavourable interference effects. As a final conclusion, we believe that the differences described in this paper between experimental results and theoretical predictions and between the wave resistance in fixed and free sinktrim conditions may be relevant at the decision-making level in early multihull hydrodynamic design. In addition, and since the hulls that have been treated are a standard and a fully defined one, we hope this paper will be useful as benchmark data for numerical analysis of multihull hydrodynamics.
Acknowledgements The research leading to these results has received funding from the Spanish Ministry for Science and Innovation with the ‘‘Programa de Acceso y Mejora de las ICTS’’, which provided funding for carrying out the experimental campaign in CEHIPAR model basin. We thank Elkin Mauricio Botia-Vera, Luise Draheim, David Feijoo de Azevedo, Carlos Ariel Garrido Mendoza, Francisco Pe´rez-Arribas, Roque Velasco-Sopranis, Hugo Gee all from our research group, and Libor Lobovsky from University of West Bohemia for their support in different tasks during the research that has led to this paper. References Broglia, R., Zaghi, S., Di Mascio, A., 2011. Numerical simulation of interference effects for a high-speed catamaran. J. Mar. Sci. Technol. 16, 254–269. Chen, X.N., Sharma, S.D., Stuntz, N., 2003. Wave reduction by S-Catamaran at supercritical speeds. J. Ship Res. 47 (2), 145–154. Insel, M., Molland, A.F., 1992. An investigation into the resistance components of high speed displacement catamarans. R. Inst. Nav. Archit. 134, 1–20. Kim, Y.H., Jenkins, D., 1981. Trim and Sinkage Effects on Wave Resistance with Series 60; cb ¼0.60. Techical report. David W. Taylor Naval Ship Research and Development Center, Bethesda, Maryland.
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Lunde, J.K., Shearer, J.R., Wieghardt, G.W., Lap, A.J., Landweber, L., Inui, T., Weinblum, G., Brard, R., 1966. Report of Resistance Commitee. Technical report. International Towing Tank Conference (ITTC). Migali, A., Miranda, S., Pensa, S., 2001. Experimental study on the efficiency of trimaran configuration for high-speed very large ships. In: Proceedings of the FAST Conference, 2001, pp. 1–5. Min, K.-S., Kang, S.-H., 2010. Study on the form factor and full-scale ship resistance prediction method. J. Mar. Sci. Technol. 15, 108–118. Molland, A.F., Wellicome, J.F., Couser, P.R., 1996. Resistance experiments on a systematic series of high speed displacement catamaran forms: variation of length–displacement ratio and breadth–draught ratio. R. Inst. Nav. Archit. 138, 55–71. Moraes, H.B., Vasconcellos, J.M., Latorre, R.G., 2004. Wave resistance for highspeed catamarans. Ocean Eng. 31 (17–18), 2253–2282. Moraes, H.B., Vasconcellos, J.M., Almeida, P.M., 2007. Multiple criteria optimisation applied to high speed catamaran preliminary design. Ocean Eng. 34 (1), 133–147. Nakatake, K., Takeshi, H., 1994. Review of program 2, inviscid flow around series 60 with free surface. In: CFD Workshop, vol. 2. pp. 130–159. Souto-Iglesias, A., Zamora-Rodrı´guez, R., Ferna´ndez-Gutie´rrez, D., Pe´rez-Rojas, L., 2007. Analysis of the wave system of a catamaran for CFD validation. Exp. Fluids 42 (2), 321–332. Tarafder, M., Suzuki, K., 2008. Numerical calculation of free-surface potential flow around a ship using the modified Rankine source panel method. Ocean Eng. 35 (5–6), 536–544. Toda, Y., Stern, F., Longo, J., 1992. Mean-flow measurements in the boundary layer and wake and wave field of a series 60 CB¼ .6 model ship—part 1: Froude numbers .16 and .316. J. Ship Res. 36 (4), 360–377. Toda, Y., Stern, F., Longo, J., 1988. Mean-flow Measurements in the Boundary Layer and Wake and Wave Field of a Series 60 Cb¼ .6 Model Ship—Part 1: Froude Numbers .16 and .316. Technical report. IIHR report no. 352. The University of Iowa, Iowa City. Todd, F.H., 1964. Series 60 Methodical Experiments with Models of Single-screw Merchant Ships. Technical report. David W. Taylor Model Basin. Turner, H., Taplin, A., 1968. The resistance of large powered catamarans. Trans. SNAME 76, 180–213. Yeung, R.W., Wan, H., 2007. Multi-hull configuration design: a framework for powering minimization. In: Proceedings of the ASME 2007 26th International Conference on Offshore Mechanics and Arctic Engineering (OMAE2007), vol. 4, pp. 833–842. Yeung, R.W., 2005. Interference resistance of Multi-hulls per thin-ship theory. In: Proceedings of the International Workshop on Water Waves and Floating Bodies. Yeung, R.W., Poupard, G., Toilliez, J.O., 2004. Interference-resistance prediction and its applications to optimal multi-hull configuration design. Trans. Soc. Nav. Archit. Mar. Eng. 112, 142–169. Zaghi, S., Broglia, R., Mascio, A.D., 2011. Analysis of the interference effects for high-speed catamarans by model tests and numerical simulations. Ocean Eng. 38 (17–18), 2110–2122.
Contents lists available at SciVerse ScienceDirect
Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Experimental assessment of interference resistance for a Series 60 catamaran in free and fixed trim-sinkage conditions Antonio Souto-Iglesias n, David Ferna´ndez-Gutie´rrez, Luis Pe´rez-Rojas Model Basin Research Group (CEHINAV), Naval Architecture Department (ETSIN), Technical University of Madrid (UPM), 28040 Madrid, Spain
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 February 2012 Accepted 3 June 2012 Editor-in-Chief: A.I. Incecik
The interference resistance of multihulls taking into account the test condition (fixed or free model) is experimentally studied. Experiments have been carried out with a commercial catamaran model and more extensively with a Series 60 catamaran. The influence of the testing condition (fixed or free) together with the influence of hull separation has been analysed. The relevance of these experimental results in the separation optimisation techniques based on slender body flow solvers is discussed. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Interference resistance Interference factor Series 60 Catamaran Free trim Fixed trim Fixed sinkage Free sinkage Free model Captive model
1. Introduction A significant body of literature analysing multihulls hydrodynamics (Chen et al., 2003; Insel and Molland, 1992; Migali et al., 2001; Molland et al., 1996; Turner and Taplin, 1968; Yeung et al., 2004), mainly considers slender body simplifications and focus on moderate and high speed regimes. Broglia et al. (2011) and Zaghi et al. (2011) use instead a Navier–Stokes solver to simulate multihulls, finding a good agreement for the resistance values and describing complex interference effects at high Froude numbers regimes. Most of these analyses assume a fixed model condition consequently reducing the computational effort. This, combined with the slender body assumption, allows for the simulation of a wider range of configurations in terms of separation and velocity for a reasonable computational effort. With these types of codes, it is therefore feasible to set up a separation optimisation framework in early design phase (Moraes et al., 2007; Yeung and Wan, 2007). In Souto-Iglesias et al. (2007), the interference resistance of multihulls was analysed by assessing its relationship with the n
Corresponding author. Tel.: þ34 913367156; fax: þ34 915442149. E-mail addresses: [email protected] (A. Souto-Iglesias), [email protected] (D. Ferna´ndez-Gutie´rrez), [email protected] (L. Pe´rez-Rojas). 0029-8018/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.oceaneng.2012.06.008
shape and amplitude of the wave train between the hulls for a specific commercial vessel design. The free model condition was then considered making it more difficult to identify interference effects due to substantially different dynamic trims and sinkages between the monohull and the catamaran. This case study is herein revisited by considering the fixed model condition. In addition to the commercial vessel, a Series-60 (S60) catamaran has been experimentally studied. Its hull shape significantly changes from the former, expanding the geometry types analysed. Although the S60 is a well known hull for experimental and computational analyses (Todd, 1964; Kim and Jenkins, 1981; Toda et al., 1988, 1992; Nakatake and Takeshi, 1994; Tarafder and Suzuki, 2008), to the authors’ knowledge, its behaviour as a multihull has not yet been experimentally described and such knowledge may be useful for CFD practitioners working on multihull hydrodynamics. In Yeung et al. (2004) the interference resistance of a S60 catamaran was numerically studied neglecting trim and sinkage influences. They provided the value of the interference factor for a wide range of separations and speeds and a significant insight into the complexity of the multihull wave interference phenomena. Their predictions have been contrasted with experimental results in the present paper. The paper is organised as follows: first, aiming at presenting the problem and the notation, the interference resistance is defined. Second, the commercial vessel case that was studied
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mh
Nomenclature
n cat cF cT cw Dzbow Dzstern g Fn IF L
catamaran friction resistance coefficient total resistance coefficient wave resistance coefficient variation of bow draft in free model condition (m) variation of stern draft in free model condition (m) gravity (m/s2) Froude number interference factor length between perpendiculars (m)
under the free trim condition in Souto-Iglesias et al. (2007) is revisited, this time, considering the fixed trim condition effect on interference resistance. Third, a S60 catamaran is analysed comparing the experimental data under fixed and free trim test conditions with the existing data found in the previously mentioned literature. Finally, a summary of the drawn conclusions together with future works are provided.
2. Interference resistance
RWcat 2RWmh 2RWmh
ð1Þ
Ideally, the value of the interference factor should be kept as small as possible, negative if achievable (Yeung and Wan, 2007). To correctly calculate the interference factor, the friction resistance has to be subtracted from the total resistance obtained in the experiments. Air drag and correlation allowance are considered negligible in the present analysis. The wave resistance is obtained via the Hughes (Lunde et al., 1966) decomposition. RT ¼ RW þ ð1þ kÞRF
ð2Þ
where k is the form factor, assumed identical for both the monohull and the catamaran cases. RF is the friction resistance of a flat plate with equivalent wetted surface, computed from the friction drag coefficient (CF) obtained via the ITTC 1957 correlation line formula: cF ¼
0:075 ðlog10 ðRe2ÞÞ2
monohull kinematic viscosity (m2/s) flat plate friction resistance (N) total resistance (N) wave resistance (N) wave resistance of monohull (N) wave resistance of catamaran (N) Reynolds number Series 60 separation (m) velocity (m/s)
wave resistance implies changing the denominator of Eq. (1) to the total resistance, since as aforementioned, friction components cancel out in the numerator. The value of the interference factor is investigated in the present paper by looking at the influence of the testing condition for two vessels, namely a commercial vessel and a Series 60 (S60). The characteristics of both models are presented in Table 1.
3. Commercial vessel
In multihulls, there is usually a strong interference between the wave systems generated by each hull. This interference can either be favourable or unfavourable to the global resistance of the hull. To properly characterise this effect, the interference factor IF is defined as the ratio of the difference between the wave resistance of the catamaran, RWcat , and twice the wave resistance force of a monohull, RWmh : IF ¼
RF RT Rw RWmh RWcat Re S60 s V
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3.1. General This vessel is commonly used in the transport of goods and fish to and from a sea farm. The main dimensions of the model are presented in Table 1. The reference system considered, the notations describing the hull separation and the vessel geometry are shown in Fig. 1. The separation (s) is defined as the distance between each hull’s centreline, and is made nondimensional with the length between perpendiculars (s/L). The free model condition studied in Souto-Iglesias et al. (2007) was aimed at finding the relationship between the interference factor Table 1 Main dimensions of the case studies. Main features
Commercial vessel
S60
Units
Length between perpendiculars (L) Beam (mh) Draft Wetted surface (mh) Displacement (mh) Block coefficient Length–beam ratio Beam–draft ratio
2.208 0.238 0.120 0.885 84.35 0.653 9.28 1.98
2.500 0.333 0.133 1.062 65.70 0.600 7.51 2.50
m m m m2 kg
ð3Þ
There is a strong dependence between the wave resistance and the value set for the form factor. This significantly affects the extrapolation procedure but moderately influences the value of the interference factor IF while maintaining its sign, the reason being that the frictional components of the resistance cancel out in the numerator of Eq. (1). Therefore, establishing whether the interference effects are favourable or unfavourable does not depend on eventual uncertainties of the form factor computation procedure. The interference factor is sometimes defined considering the total resistance (Zaghi et al., 2011). According to the Hughes resistance decomposition, using the total resistance instead of the
Fig. 1. Commercial vessel model geometry and reference system.
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and the amplitude of the wave system in between the two hulls. The present study completes the previously mentioned work by performing tests in fixed model condition using this geometry, thus eliminating the effects of sinkage and trim movements. A photograph taken during the tests of this paper’s experimental campaign is shown in Fig. 2. Further information about this hull is included in Souto-Iglesias et al. (2007) including its 3D geometrical definition as an IGES file, provided as a supplementary material. The following tests were carried out:
Monohull, free model Monohull, fixed model Catamaran, s/L¼ 0.388, in free model condition Catamaran, s/L¼ 0.388, in fixed model condition
The separation (s/L¼0.388) was chosen for having the most interesting interference effects, as found in Souto-Iglesias et al. (2007). A test matrix comprising of the speeds shown in Table 2 was initially devised. The speed range of main interest corresponds to Froude numbers between 0.2 and 0.4. For the Froude number 0.375 the experiment was repeated 5 times in order to assure that measurement uncertainties remain considerably smaller than the interference effects to analyse. A collection of extra velocities was run for the range 0.3 oFno0.4 in order to
Fig. 2. Picture of commercial vessel-model test.
Table 2 Froude numbers and velocities considered for the commercial vessel tests. Point
Fn
V (m/s)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0.100 0.150 0.200 0.250 0.300 0.350 0.375 0.375 0.375 0.375 0.375 0.400 0.450 0.500 0.550
0.465 0.698 0.931 1.164 1.396 1.629 1.745 1.745 1.745 1.745 1.745 1.862 2.094 2.327 2.560
properly characterise the resistance hump. Videos of these experiments, provided as supplementary material, can be found online at http://canal.etsin.upm.es/ftp/2012/S60/ 3.2. Results The resulting experimental curves are presented in Fig. 3. It can be observed that there is a significant difference in the results for the fixed and free model conditions, with the free model resistance being larger than the fixed model in all cases, as in Kim and Jenkins (1981) for a S60 monohull and Moraes et al. (2004) for the Wigley hull. With regard to the differences between monohull and catamaran, the tendency in the monohull resistance is monotonic whilst a clear hump can be appreciated for the catamaran configuration. Focusing on the hump region, these characteristics are discussed in detail in what follows next. In order to adequately estimate the interference factor for a continuous range of Froude numbers, the resistance curves were fitted with NURBS (Fig. 4 left and right). In these figures, the markers correspond to the raw experimental data. The interference factor refers to a comparison between wave resistances which have been obtained from the total resistance following the procedure described in Section 2 and considering a form factor of 0.24. The form factor has been taken as the same for the catamaran and the monohull. Fig. 4 left and right show the differences in wave and total resistance in the hump region (0.3oFno0.4) between the monohull and the catamaran for the free and fixed model conditions respectively. It can be seen that the wave resistance and the total resistance follow a similar trend, although as previously mentioned, the values remain lower for the fixed trim condition. Favourable interference regions corresponding to those where the catamaran resistance is smaller than twice that of the monohull can also be observed. The interference factor is calculated from these data with the results shown in Fig. 5. While it is apparent that the values are different for 0.3 oFno0.34, a very similar pattern is obtained for Fn40.34. Overall, the tendency of the interference factors for the free and fixed model conditions is similar, with some differences in the IF values for the Froude numbers between 0.3 and 0.34. This fits with what was expected from analysing the trim angles of the monohull and catamaran configurations in free model condition, as discussed in Souto-Iglesias et al. (2007). Results regarding sinkage and trim are presented in Fig. 6. They are made nondimensional using the typical length V2/g (Eqs. (4) and (5)), as in Kim and Jenkins (1981). Trim ¼ ðDzbow Dzstern Þ2g=V 2
ð4Þ
Sinkage ¼ ðDzbow þ Dzstern Þg=V 2
ð5Þ
Fig. 3. Total resistance of commercial vessel, s/L¼ 0.388.
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Fig. 4. Total and wave resistance, commercial vessel, free (left) and fixed (right) conditions.
Fig. 5. IF of commercial vessel for test case s/L¼ 0.388. Fig. 7. S60 catamaran model.
Fig. 6. Sinkage and trim, commercial vessel.
This typical length is the characteristic wave length over 2p. Although the sinkage is significant (o10% of the draft), its behaviour is very similar for both the monohull and the catamaran. If we look at the trim, absolute trim angles remain small (between 0.31 and 0.31, equivalent to 70.06 in the nondimensional trim from Fig. 6) with small variations. The trim angle reduction around Fn¼0.37 for the catamaran may help in explaining the favourable interference found in the free model condition for this velocity.
4. Series 60 4.1. General The tests have been carried out with a Series 60 (Todd, 1964) catamaran (fig. 7). The model characteristics have been presented in Table 1 together with those of the commercial vessel test case. The dimension ratios are fairly similar for these two vessels but
Fig. 8. S60 (Todd, 1964) body plan (black) and present study (red). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
the hulls are significantly different: 1. The S60 has no cylindrical section compared to a long one for the commercial vessel. 2. The S60 has a conventional cruise type aft body and the commercial vessel has a transom stern. 3. The S60 has no knuckles while the the commercial vessel has a hard chin. Prior to the milling of the models, the hull geometry was computationally redefined starting from the IGES definition used
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as benchmark in the Tokyo 1994 CFD Workshop. The reason for this refairing is that too many surface patches with not enough quality matching were used in the latter. Furthermore, a vertical extension of the model was required to cope with the generated waves from high Froude number tests. The matching of the updated geometry with the original S60 definition (Todd, 1964) is good, as can be appreciated in Fig. 8. The IGES file used here is provided as a supplementary material at http://canal.etsin.upm. es/ftp/2012/S60/, with the aim to serve as a standard digital definition for further studies. The following separations have been tested: a) b) c) d)
s¼0.565 m, s/L¼0.226 s¼0.768 m, s/L¼0.307 s¼0.971 m, s/L¼0.388 s¼0.1174 m, s/L¼0.470
The rationale behind this selection is that, according to the computational analysis of a Series 60 catamaran by Yeung et al. (2004), s/L¼ 0.226 was determined as the separation ratio for which the largest favourable interferences take place. s/L¼0.388 is the separation ratio with the largest favourable interference effects for the commercial vessel case studied in the previous section. s/L¼0.307 is the mean value of 0.226 and 0.388. s/L¼0.470 is larger than 0.388 and chosen to evenly space the 4 separations. Results are presented and discussed for each of these 4 separations. The form factor used for the computation of the wave component of the resistance is taken as 0.0673. This value was deduced by Min and Kang (2010) who undertook a very thorough study on the dependence between the form factor and the Reynolds number. As for the commercial vessel, it is assumed that the form factor for the monohull and the catamaran is the same. The velocities presented in Table 3 were run for the monohull and for the catamaran with all four separations in both free and fixed model conditions. On top of the points presented in Table 3, a total of 5 extra runs were done for the regions of convexity change in the resistance curves. These extra points are shown in the resistance curves in the next section. Since it was previously
unclear where the strongest interference effects would take place, the range of Froude numbers is wider than the one used for the commercial vessel (Table 2). The videos of these experiments, provided as a supplementary material, can be found online at http://canal.etsin.upm.es/ftp/2012/S60/. A photograph taken during the experiments is presented in Fig. 9.
4.2. Resistance curves for all separations The resistance curves for the monohull and the catamaran with all 4 separations in fixed and free model conditions are presented in Figs. 10 and 11. There is a slight hump in the resistance curves for both fixed and free model conditions for 0.3oFn o0.4. In both conditions and as a general trend, the resistance diminishes as the separation increases, tending to that of the monohull. Let us point out that the monohull resistance has been doubled for the comparison. The translation of these results in the interference factor is later discussed.
Fig. 9. Picture of S60 model test.
Table 3 Froude numbers and velocities for the S60 catamaran tests. Point
Fn
V (m/s)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0.15 0.20 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.45 0.50 0.55
0.743 0.990 1.238 1.288 1.337 1.387 1.436 1.486 1.535 1.585 1.634 1.684 1.733 1.783 1.832 1.882 1.931 1.981 2.030 2.080 2.129 2.229 2.476 2.724
Fig. 10. S60, total resistance in free model condition.
Fig. 11. S60, total resistance in fixed model condition.
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4.3. Resistance curves in free and fixed model conditions The graphs in Fig. 12 show the resistance curves for each separation in fixed and free model conditions, and compare them
43
with the monohull ones. As a general trend, it can be observed that the resistance is greater in the free model condition than in the fixed one for each separation. This is best appreciated when comparing the data for the greatest speed. In Section 3.2, a similar effect is described
Fig. 12. S60, total resistance in fixed and free model conditions. Top left: s/L=0.226, Top Right: s/L=0.307, Down left: s/L=0.388, Down Right: s/L=0.470.
Fig. 13. S60, total and wave resistance in free model condition. Top left: s/L=0.226, Top Right: s/L=0.307, Down left: s/L=0.388, Down Right: s/L=0.470.
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for the commercial vessel. As can be appreciated in Fig. 12, the differences are larger for the catamaran than for the monohull and even larger for small separations compared to large ones. This effect was also described for the Wigley hull by Moraes et al. (2004).
For the catamaran in free model condition, with s/L¼0.226, the greatest speeds could not be reached due to the generated waves entering the model. For s/L¼0.307 in free model condition, the planning range for the catamaran configuration is reached.
Fig. 14. S60, total and wave resistance in fixed model condition. Top left: s/L=0.226, Top Right: s/L=0.307, Down left: s/L=0.388, Down Right: s/L=0.470.
Fig. 15. IF for the S60. Top left: s/L=0.226, Top Right: s/L=0.307, Down left: s/L=0.388, Down Right: s/L=0.470.
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This can be deduced by looking at the flattening of the resistance curve for Fn¼0.55. For s/L¼0.388, the difference in resistance values between the monohull and the catamaran grows smaller for large Froude numbers both in fixed and free model conditions. This tendency is made clearer with the largest separation (s/L¼0.470). 4.4. Wave resistance In order to calculate the interference factor for a continuous range of Froude numbers, the resistance curves have been fitted with NURBS. For each case, wave resistances have been obtained from the total resistance following the procedure described in Section 2. The curves representing these results are shown in Figs. 13 and 14 for free and fixed model conditions respectively. In these figures, the markers correspond to the raw experimental data. Data are presented for Fn4 0.3, where the first behaviour differences between the monohull and the catamaran start to take place. We can conclude that for the free model condition and smallest separation, there is no favourable interference region. For the largest Froude numbers the catamaran and the monohull resistances tend to converge. In the mid part of the graphs the trends are more intricate and described through the IF in the next section. 4.5. Interference factor Using the wave resistance curves presented in the previous section, the interference factors for both fixed and free model conditions and for all separations are presented in this section.
45
Results are compared with Yeung et al. (2004) and Yeung (2005), who considered a thin-ship potential approximation to model the problem, with a fixed model hypothesis. Interference factors for free and fixed model conditions are presented for all separations in Fig. 15. Focusing on s/L¼0.226, it can be appreciated that the free model and fixed model interference factors are significantly different. Although according to Yeung et al. (2004), where this last separation with Fn¼0.33 produces the most favourable interference effects, this does not occur in the present experiments. For Fn¼ 0.33 the interference is unfavourable and the minimum is shifted to around Fn¼0.38. The free model condition presents overall a more unfavourable behaviour than both fixed condition and theoretical model. This is relevant since in real applications, the free model condition applies. For the largest velocities there is a convergence between the fixed model condition results and those of Yeung et al. (2004). For s/L¼ 0.307, it can be appreciated that the free model interference factor significantly differs from the fixed model one in the range 0.35oFno0.4. With regards to the comparison with Yeung et al. (2004), it is noticeable that the peak value of the interference coefficient is shifted to 0.05 (from 0.38 to 0.43 in the experimental results). This shift is also present in the minimum value of the interference factor. For the largest velocities there is a convergence between the experimental results and those from Yeung et al. (2004) in free and fixed model conditions. Furthermore, the interference effects diminish and the IF tends to zero, as is the case in Zaghi et al. (2011). Analogously to what happened for the commercial vessel, in the S60 case, the strongest favourable interference effects are found for s/L¼0.388. With regards to the comparison with Yeung
Fig. 16. Contour plot as function of Fn and s/L of the IF for the S60. Top: Yeung et al., (2004), Down Right: Free model, Down left: Fixed model.
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et al. (2004), the peaks and valleys in the experiments are delayed with respect to the model. For the largest velocities, the convergence of the experimental results found in this paper to those of Yeung et al. (2004) is clearly appreciated. More attenuated trends are observed for the largest separation, s/L¼ 0.470. An interesting global representation of these effects across the different separations is given. To do this, a contour projection of the 3D graph for the IF is presented in Fig. 16. The tendencies observed in the individual graphs for each separation (Fig. 15) are now clearer. The colour scale in each graph is individualised due to the range of the interference factor data from Yeung et al. (2004) being significantly shorter than the one found experimentally. Globally there are some similitudes in the interference patterns but some differences can be appreciated. Comparing the free model experimental data (which is the realistic configuration to be found in full scale) with those of Yeung et al. (2004) shows that the most favourable interference takes place at a similar Fn (0.33) and with a similar IF (around 0.2) but at a larger separation (0.4 instead of 0.226). This Fn is similar to that found by Zaghi et al. (2011) with a slenderer model. The unfavourable interferences are stronger in the experimental case with a maximum of the order of 0.7 instead of the theoretically calculated 0.3. It is significant that this maximum does not take place for the smallest separation, as is the case in Zaghi et al. (2011). Also, in experiments, there is a smoother transition between the favourable and unfavourable regions compared to the theoretical model. Now comparing free and fixed model condition tests, other differences can be appreciated: 1. The transition between favourable and unfavourable regions is sharper for the fixed model case. Such a sharp transition in the fixed model case is predicted by the theoretical model. 2. For the smallest separations and contrary to what happens in the free model condition, there are favourable, although quite mild, interference regions in the fixed model condition results. 3. Although the unfavourable interference regions are similar in size, the free model ones are more intense. 4. The most favourable interference factor in fixed model condition is smaller than the free model one.
Fig. 17. Sinkage for the S60.
Fig. 18. Trim for the S60.
Looking at the trim (Fig. 18) and in all cases, the differences are more patent for larger Fn. Between Fn¼0.38 and Fn¼0.45 a significant trim increase is appreciated. This shift requires further investigation in order to evaluate a possible relation between differences in the IF in free and fixed model condition.
5. Conclusions Summarizing, the free model condition tends to enhance the favourable and unfavourable interference effects. 4.6. Sinkage and trim The object of this section is to analyse the relationship between the IF differences in free and fixed model conditions and the dynamic position (sinkage and trim) in free model condition. It is also relevant to analyse differences in sinkage and trim in free model condition between the monohull and the catamaran; such values are presented in nondimensional form in Figs. 17 and 18, following the definitions by Kim and Jenkins (1981) presented in Eqs. (4) and (5). When comparing the S60 data with those of the commercial vessel (Fig. 6), sinkage seems to be of the same order but trim is significantly larger for the S60. Pending future work, we believe this may have an influence on the IF behaviour change between fixed and free model conditions. When comparing the S60 monohull and the S60 catamaran in free model condition, large differences in sinkage can be appreciated for 0.3 oFno0.42 (Fig. 17). For the shortest separation (s/L¼0.226) the sinkage for the catamaran is around 50% greater. Also for s/L¼0.226, as can be seen in Fig. 15, the differences in the IF between free and fixed model are significant but not monotonic, unlike the sinkage differences, which are monotonic.
The interference resistance of multihulls taking into account the testing condition (fixed model or free model) has been experimentally studied. Experiments have been carried out with a commercial catamaran model and more extensively with a Series 60 catamaran. For the commercial vessel, the influence of the model condition has been analysed for the separation in which the strongest interference effects take place. In this case it has been shown that the influence of the model condition (freefixed) is not substantial. This is consistent with the experiments presenting moderate dynamic trim-sinkage values and small differences in dynamic trim and sinkage between the monohull and the multihull configuration in free model condition. For the Series 60 model a range of separations has been studied and compared with the fixed model slender body theoretical results. The differences between the free and fixed condition experimental results are significant, with the free condition providing more extreme cases in the favourable and unfavourable interference regimes. The optimum interference factor ( 0.2) appears at a Froude number of 0.33, agreeing with theoretical results. Nonetheless, this optimum interference occurs for a substantially larger separation ratio (0.40) than the theoretically predicted (0.226). The transition between favourable and unfavourable regions is sharper for the fixed model case. Such a sharp transition is in accordance with the theoretical model predictions. For the smallest separation and
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contrary to what happens in the free model condition, there are favourable, although quite mild, interference regions in the fixed model condition. It has been described that for each separation there is a shift in the maximum favourable and unfavourable interference Froude numbers as compared to the theoretical model. In general, the free model condition tends to enhance the favourable and unfavourable interference effects. As a final conclusion, we believe that the differences described in this paper between experimental results and theoretical predictions and between the wave resistance in fixed and free sinktrim conditions may be relevant at the decision-making level in early multihull hydrodynamic design. In addition, and since the hulls that have been treated are a standard and a fully defined one, we hope this paper will be useful as benchmark data for numerical analysis of multihull hydrodynamics.
Acknowledgements The research leading to these results has received funding from the Spanish Ministry for Science and Innovation with the ‘‘Programa de Acceso y Mejora de las ICTS’’, which provided funding for carrying out the experimental campaign in CEHIPAR model basin. We thank Elkin Mauricio Botia-Vera, Luise Draheim, David Feijoo de Azevedo, Carlos Ariel Garrido Mendoza, Francisco Pe´rez-Arribas, Roque Velasco-Sopranis, Hugo Gee all from our research group, and Libor Lobovsky from University of West Bohemia for their support in different tasks during the research that has led to this paper. References Broglia, R., Zaghi, S., Di Mascio, A., 2011. Numerical simulation of interference effects for a high-speed catamaran. J. Mar. Sci. Technol. 16, 254–269. Chen, X.N., Sharma, S.D., Stuntz, N., 2003. Wave reduction by S-Catamaran at supercritical speeds. J. Ship Res. 47 (2), 145–154. Insel, M., Molland, A.F., 1992. An investigation into the resistance components of high speed displacement catamarans. R. Inst. Nav. Archit. 134, 1–20. Kim, Y.H., Jenkins, D., 1981. Trim and Sinkage Effects on Wave Resistance with Series 60; cb ¼0.60. Techical report. David W. Taylor Naval Ship Research and Development Center, Bethesda, Maryland.
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