流体中における円柱の偏心回転運動(第1報)

概要

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As shown in Fig. 1,when a cylinder, which is rotating around its own axis O' with an angular velocity Ω, revolves around a fixed axis O with a constant angular velocity ω, the stream function Ψ'is Ψ'(γ', α) where α=θ-ωt'-π/2. In this case the equation of motion of fluid is expressed by Eq. (3) and in non-dimensional form, by Eq. (4). Now we assume Ψ as Eq. (8) and determine 16 unknown coefficients as satisfy Eq. (4) and the boundary conditions (5) and (6). That is, from Eqs. (13)〜(16), we determine A_1,A_3,B_2,B_4 neglecting A2,A_4,B_1,B_3 which are small comparing with the others, and then determine A_2,A_4 B_1,B_3 from Eqs. (11), (12), (17) and (18). And the other coefficients can be determined from Eq. (9). Some numerical examples are shown in the Tables and the Figures, and the experimental results are also shown in the photographs.
1958-05-25