• Journal of the Korean Society for Aviation and Aeronautics
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• v.21 no.1
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• pp.45-50
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• 2013

In this study, lumped-vortex element method and thin airfoil theory were used to analyze aerodynamic characteristics of airfoils with relative motion that had camber lines of NACA $44{\times}{\times}$ airfoil in 2-dimensional unsteady incompressible potential flow. Velocity disturbance due to airfoil was calculated by lumped-vortex element model and force distribution on airfoil by unsteady Bernoulli's equation. Variables in relative motion were considered the period p, the amplitude of flapping $A_f$ and pitching $A_p$, and the phase difference between flapping and pitching ${\phi}_p$ and the angle of attack ${\alpha}$. Due to movement of an airfoil, dag was induced in 2-dimensional unsteady incompressible potential flow. The numerical results show that the aerodynamic characteristics of the airfoil with flapping and pitching at the same time are illustrated. Especially the mean lift coefficient became smaller, but drag coefficient became larger.

• Ocean Systems Engineering
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• v.14 no.3
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• pp.301-314
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• 2024

In this study, the lift coefficient and wave deformations for a two-dimensional flat-plate in non-cavitating condition were computed using a closed-form (analytic) solution. This plate moves at a constant speed beneath a free surface in water of finite depth. The model represents the flat-plate using a lumped vortex element within the constraints of potential flow theory. The kinematic and dynamic free surface conditions were combined and linearized. This linearized free surface condition was then applied to get the total velocity potential. The method of images was utilized to account for the effects of finite depth in the calculations. The lift coefficient of the flat-plate and wave elevations on the free surface were calculated using the closed-form solution. The lift coefficients derived from the present analytic solution were validated by comparing them with Plotkin's method in the case of deep water. Wave elevations were also compared with those obtained from a numerical method. A comprehensive discussion on the impact of Froude number, submergence depth of flat-plate from the calm free surface, the angle of attack and the depths of finite bottom on the results - namely, lift coefficients and free surface deformations - is provided.