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Potential flow of a second-order fluid over a tri-axial ellipsoid

F. Viana1, T. Funada2, D.D. Joseph1, N. Tashiro2 & Y. Sonoda2

1Department of Aerospace Engineering and Mechanics, University of Minnesota, 110 Union St. SE, Minneapolis, MN 55455, USA

2Department of Digital Engineering, Numazu College of Technology, 3600 Ooka, Numazu, Shizouka, 410-8501, Japan



The problem of potential flow of a second-order fluid around an ellipsoid is solved, following general expressions in Lamb (1993), and the flow and stress fields are computed. The flow fields are determined by the harmonic potential but the stress fields depend on viscosity and the parameters of the second-order fluid. The stress fields on the surface of a tri-axial ellipsoid depend strongly on the ratios of principal axes and are such as to suggest the formation of gas bubble with a round flat nose and two-dimensional cusped trailing edge. A thin flat trailing edge gives rise to a large stress which makes the thin trailing edge thinner.

Keywords: Potential flow, Second-order fluid, Cusp, Normal extensional stress