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Modification of Rheological Responses under Elongational Flow
Published in S. T. Lee, Polymeric Foams, 2022
Masayuki Yamaguchi, Jiraporn Seemork, Monchai Siriprumpoonthum, Tadashi Yokohara, Bin Md Ali Mohd Amran, Panitha Phulkerd
The elongational viscosity values in Figure 2.16 correspond qualitatively with the slender-body theory prediction (Equation 2.7) [94]. Furthermore, the viscosity curves were quantitatively calculated from the simulation results, which gave information on the importance of the viscosity ratio [95,96]. This mechanism is applicable to various polymer blends, in which a dispersed phase exhibits strain hardening in elongational viscosity, such as LLDPE containing LCB-PP as a dispersed phase [97], and PLA containing ethylene-vinyl acetate copolymer (EVA) as a dispersed phase [98]. In the latter case, the mechanical properties in the solid state, especially fracture energy, are also greatly improved owing to the favorable compatibility of the components. The fine dispersion of droplets leads to shear yielding of the continuous PLA phase, while the weak cohesive strength of EVA results in cavitation and thus reduced dilatational stress in the solid state [103].
CFD-based empirical formulae for squat prediction of modern container ships
Published in Ship Technology Research, 2022
Zhen Kok, Jonathan Duffy, Shuhong Chai, Yuting Jin
Different theoretical methods have been developed to predict ship squat. Most of the early theoretical methods involved prediction of water-level depression to estimate squat via the continuity equation such as that of Constantine (1960), Balanin and Bykov (1965), Tothill (1967), McNown (1976) and Gates and Herbich (1977). Perhaps the most well-known theoretical method is the slender body theory developed by Tuck (1966). Tuck’s formula became the foundation for the development of many other methods, some of which can be considered as semi-empirical methods. For example, Tuck’s formula was modified by Hooft (1974) to estimate bow squat. Huuska (1976) then conducted experiments in restricted shallow water conditions to derive a correction factor for blockage effect. Similarly, Vermeer (1977) modified Tuck’s formulae to account for narrow canals. A three-dimensional squat theory for water of finite depth and width was later developed by Tuck and Taylor (1970). Naghdi and Rubin (1984) used non-linear steady-state solution of the differential equation of the slender-body theory to predict squat in shallow water. Cong and Hsiung (1991) then consolidated the slender-body theory and flat ship theory to predict squat for transom stern ships.
Establishment of a design study for comprehensive hydrodynamic optimisation in the preliminary stage of the ship design
Published in Ships and Offshore Structures, 2023
Myo Zin Aung, Amin Nazemian, Evangelos Boulougouris, Haibin Wang, Suleyman Duman, Xue Xu
The use of linear, slender body theory is a common approach in the numerical modelling of wave resistance for slender hull types, such as ships and submarines. This is because these methods can provide fast and accurate solutions to the wave resistance problem for these types of hulls. The hull shape can be approximated as a three-dimensional panel mesh that is uniform along the length of the hull. Numerical models that use linear, slender body theory typically involve discretising the hull into a series of panels and then solving for the flow around each panel using potential flow theory. The solutions for each panel are then combined to calculate the total wave resistance of the hull.
Distribution and penetration efficiency of cylindrical nanoparticles in turbulent flows through a curved tube
Published in Aerosol Science and Technology, 2020
Jianzhong Lin, Ruifang Shi, Fangyang Yuan, Mingzhou Yu
The motion of cylindrical particle is modeled based on the slender-body theory (Batchelor 1970), i.e., the disturbance motion induced by the cylindrical particle is approximately the same as that induced by a line distribution of Stokeslets. A Stokeslet is a singularity in the Stokes flow and represents the effect of a force applied to the fluid at a point. In the slender-body theory, the cylinder is divided into several segments and the force exerted on a segment is represented by a point force. Although the force acting on a point is isotropic, the force acting on the whole cylinder is non-isotropic.