Numerical Investigation into the Pressure and Flow Velocity Distributions of a Slender-Body Catamaran Due to Viscous Interference Effects

A computational fluid dynamics investigation was carried out on a slender body catamaran to determine the effect of pressure and flow velocity changes for varied hull separations. The investigation was conducted using an NPL 4a model with a slenderness (length to breadth) ratio of about 11 together with the use of a commercial code (CFX) with hull separations of S/L = 0.3 and 0.4 along with a variation in Reynolds numbers of 2.86×105, 3.43×105, 4.01×105, and 4.44×105. Pressure and flow velocity around the hull were measured to obtain a fluid effect attributed to the influence of catamaran hull interference. A computational fluid dynamics investigation was carried out with the same configurations as those in the experimental tests. The overall results were in good agreement, with the order of discrepancy at about 1.76%; the computational fluid dynamics results were consistently lower than the experimental ones. Both tests demonstrated a viscous interaction between the hulls and, thus, the form factors for the demihull and catamaran were properly derived: the form factor for the demihull (1+k) was 1.254 and for the catamaran (1+?k) was 1.420, indicating interaction effects of about 13.2%. The form factor for the catamaran was consistently higher than the demihull, suggesting some viscous interference between the hulls. The effect of catamaran hull interference variation can be recognized through the velocity augmentation ratio (?), pressure change ratio (?), and the viscous interference factor (?). In addition, the ? value is very helpful for finding out the interference of the hull on a catamaran when sophisticated experimental and numerical tools are not available.

Catamaran; CFD; Flow velocity; Pressure distribution; Viscous interference factor

In the last 50 years, the development of catamaran theory has been proposed by many researchers to explain the resistance of catamarans. The reflex model was a technique pioneered by Joubert and Matheson (1970), where the resistance of the hull was measured in a wind tunnel. Utama (1999) conducted a detailed experimental investigation in a low-speed wind tunnel on a single ellipsoid (as a reflex model) and a pair of ellipsoids nearby representing a catamaran. Theoretical, numerical, and experimental investigations have been carried out on multihull vessels and further research has been conducted by Zaghi et al. (2011).

An increasing number of researchers are calculating ship resistance using CFD. Broglia et al. (2014) completed a study on catamarans with Froude numbers between 0.3 and 0.5 which showed that the configuration of the narrow hull distance between catamarans has a more significant interference effect. Numerical computation to illustrate the hydrodynamic factors that influence ship resistance using a FLUENT code has been investigated by Deng et al. (2011). Jamaluddin et al. (2013) conducted experimental and numerical investigations to analyze the components of resistance and interactions between hulls in catamarans, and Samuel et al. (2015) studied the selection of optimal catamaran hulls on traditional fishing vessels.

Previous studies have discussed a lot of catamaran hull interference, but not many have conducted detailed research related to interference due to viscous form factors. Broglia et al. (2019) have been conducting research to improve the capabilities of state-of-the-art CFD tools in the prediction of the flow-field around a multihull catamaran.  Viscous resistance represents an integral part of the total resistance of a catamaran in which intermediate Froude Number value interference effects are dominant (Farkas et al., 2017). A potential-flow method was carried out to determine the lift force of single-deadrise hulls and catamaran configurations in which hydrodynamics pressure was more pronounced between two catamaran hulls (Bari and Matveev, 2017). Iqbal and Samuel, (2017) have conducted research catamaran hull form show that the fluid form that surrounds the ship hull influences ship resistance. Mittendorf and Papanikolaou (2020)  investigated catamaran resistance and also found an increase in total resistance due to viscous interference. Therefore, the CFD technique could be used to optimize the hull of a catamaran (Miao et al., 2020; Yongxing and Kim, 2020).

The study objectives were to determine the viscous interference due to pressure and flow velocity changes between the catamaran hulls by using a reflex model and to derive viscous form factors (?) in the catamaran models using CFD. The results were validated with an experimental investigation which was carried out in a wind tunnel on a symmetrical catamaran using a reflex model of NPL4a by Jamaluddin et al. (2013).

The effects of two variations of hull separations for a catamaran, which were investigated by CFD analysis, were compared with a wind tunnel experiment to validate the results. Numerical simulation and experiment (wind tunnel) results show a relatively small difference in the value of flow and pressure components, which is 1.76% on average. This result shows consistency and is entirely accurate. The difference in viscous resistance is about 13.2%, where the catamaran resistance is greater than that of the demihull and is attributed to the interaction between the hulls of the catamaran. The numerical simulation clearly illustrates the change in flow at the inner hulls which causes the result that viscous resistance at S/L = 0.3 is higher than that at S/L = 0.4. Also, it applies to the pressure acting on the model catamaran; the viscous pressure increases as the S/L decreases. The effect of the catamaran hull interference variation can be recognized through the velocity augmentation ratio (?), pressure change ratio (?), and viscous interference factor (?). The influence of interference resistance between two ship hulls causes the symmetrical flow of water around the demihull to be asymmetrical due to high pressure (which relates to s) and flow velocity (associated with f) which occurs around the hull and is relatively unequal to the hull centerline. In addition, the ? value is very helpful for finding out the hull interference on a catamaran when sophisticated experimental and numerical tools are not available.

The authors wish to thank the Ministry of Research, Technology, and Higher Education (Kemristekdikti) and the Institut Teknologi Sepuluh Nopember (ITS) for funding the current work under a scheme called the World-Class Professor (WCP) Program with the contract number T/42/D2.3/KK.04.05/2019.

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