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2 Bulletin of the Polish Academy of Sciences. Technical Sciences

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On Plane, Steady, Creeping Flow, Generated Around an Arbitrary Cylinder by a Translating Flat Plate

Klonowska-Prosnak M.E., Prosnak W.J., Cześnik P.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2003

Vol. 51, nr 2

113-144

Plane, steady, creeping flow around an arbitrary cylinder situated in vicinity of a flat plate is considered, the flow being generated by translation of this plate along itself with constant speed, perpendicular to generatrices. The stream function of the flow satisfies the biharmonic equation, so that all properties of the flow - such as velocity and pressure fields as well as fields of other stress tensor components - are expressed in terms of the Goursat functions. Hence, the problem of determination of the flow reduces to determination of these functions. The two-step approach is applied to the solution of this problem. The first step consists in conformal mapping of the original domain of solution onto an annulus - by means of a suitable set of mapping functions. The second step consists in development of the two Goursat functions in Laurent series extended by two logarithmic terms each. Unknown coefficients of the series have to satisfy a system of linear algebraic equations, following from boundary conditions. The system is arrived at by means of the pseudospectral method. The so obtained velocity field is applied to generation of streamline patterns. Such a pattern is presented in the paper, and compared with an analogous one, corresponding to potential flow.

Remarks on Plane, Steady, Creeping Flows Generated by Singularities

Klonowska-Prosnak M.E., Cześnik P.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2002

Vol. 50, Nr 1

45--69

Two properties of plane, steady, creeping flow generated in the infinite domain around a given contour by a single singularity are investigated in the paper. The first property concerns velocity field. It is shown, that stream uniform at infinity must occur automatically in this case, and formulae for velocity of the stream are derived. The second property concerns similarity of streamline pattern of such flow, and the potential one, generated around the same contour by the same singularity. Investigation of the both properties concerns - in particular: a disc, an ellipse and the airfoil sections NACA 0012, RAE 2822.