Analytical solutions for uniform potential flow past multiple cylinders
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Cited by (76)
Hydrodynamic interaction between two polygonal cylinders in uniform potential flow
2023, Ocean EngineeringComputation of plane potential flow around multi-element airfoils using the Schottky–Klein prime function
2023, Physica D: Nonlinear PhenomenaPotential flow around polygonal shaped cylinders using hypotrochoidal mapping function
2022, International Journal of Mechanical SciencesCitation Excerpt :The potential flow is classically used to describe the velocity field and pressure profile on aerofoils, water waves, groundwater flow, electro-osmotic flow, etc. To model uniform potential flow around a circular cylinder and non-uniform potential flow due to presence of point singularity (vortex or doublet) outside a cylinder, complex potential function can be derived using Milne-Thomson circle theorem [44,45]. The potential flow obtained by above complex potential function in simply connected domain Dζ inside unit circular disc can be conformaly mapped to the domain Dz outside of unit circular disc by using mapping function Z(ζ) = 1/ζ (a point β ∈ Dζ maps to zβ ∈ DZ).
Potential flow in a multiply connected circle domain using series methods
2021, Journal of Computational and Applied MathematicsNew estimations of the added mass and damping of two cylinders vibrating in a viscous fluid, from theoretical and numerical approaches
2020, Journal of Fluids and StructuresCitation Excerpt :However, in many practical situations, the effects of fluid viscosity and compressibility are neglected and a potential theory is carried out. A method of images (Hicks, 1879; Greenhill, 1882; Basset, 1888; Carpenter, 1958; Birkhoff, 1960; Gibert and Sagner, 1980; Landweber and Shahshahan, 1991) or a complex analysis based on conformal transformations (Wang, 2004; Burton et al., 2004; Tchieu et al., 2010; Scolan and Etienne, 2008; Crowdy, 2006, 2010) are usually derived to solve the boundary value problem governing the fluid potential function. For small amplitude motions not entailing flow separation, the potential theory will accurately give the added mass coefficients, and tabulated results are available in the literature for a wide variety of immersed geometries (Patton, 1965).
Computation of plane potential flow past multi-element airfoils using conformal mapping, revisited
2019, Journal of Computational and Applied Mathematics